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Physics Laboratory Manual Equipotential and Electric Field Lines

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Equipotential and Electric Field Lines

Student’s Guide

Laboratory Manual

(2017)


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PACKING LIST

1. Black Conductive Paper

2. DC Power Supply

3. Multimeter (Voltmeter)

4. Graph Paper

5. Corkboard

6. Pushpins

7. Connecting Wires

8. Standard Power Cable

9. Student and Teacher Manuals


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Contents

1. Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2. Electric Potential and Potential Difference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3. Electric Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4. Electric Potential Due to Point Charges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

5. Relation between Electric Potential and Electric Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

6. Equipotential Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

7. Electric Fields and Conductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

8. Experimental Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

9. Laboratory Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20


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The objectives of this laboratory experiment are;

1) To study the relation between the equipotential

lines and electric field,

2) To investigate and map the equipotential lines of

two oppositely charged conductors,

3) To plot the electric field lines using the

equipotential lines in two dimensions,

4) To study the effect of a conducting ring on the

equipotential and electric field lines.

An electric charge exerts a force of attraction or

repulsion on other electric charges. The force a

charged object exerts on a second one is proportional

to the product of the magnitude of the charge on one

( ) times the magnitude of the charge on the other

( ), and inversely proportional to the square of the

distance between them. As an equation, we can

write the electrostatic force between any two charges

as;

(1)

This is the Coulomb’s law. In this expression is

proportionality constant. Coulomb’s law, Equation-(1),

gives the magnitude of the electric force that either

charge exerts on the other. Keep in mind that

Equation-(1) represents the force on a charge due to

only one other charge, a distance apart. The

direction of the electric force is always along the line

joining the two charges. If the two charges have the

same sign, the force on either charge is directed away

from the other (that is, they repel each other). However,

if the two charges have opposite signs, the force on

one is directed toward the other (they attract).

Figure-1: Work is done by the electric field in moving the

positive test charge from the position to the position

. Electric field lines are parallel and equally spaced in

the central region.

The constant is often written in terms of another

constant called the permittivity of free space. It is

related to by ⁄ . So, the electrostatic force

can be rewritten as;

(2)

where,

We can define the potential energy for the

electrostatic force. Consider the electric field

between two equally but oppositely charged parallel

plates (Figure-1). Also consider a positive point charge

placed at point a very near the positive plate. If this

charge at point is released, the electric force will

do work on the charge and accelerate it toward the

negative plate.

1. Purpose

2. Electric Potential and Potential Difference


5

The work done by the electric field to move the

charge a distance is given by;

(3)

where we used the relation, .

The change in electric potential energy equals the

negative of the work done by the electric force;

(4)

This means that the potential decreases (that is, is

negative). As the charged particle accelerates from

point to point , the particle’s kinetic energy

increases. According to the conservation of energy,

electric potential energy is transformed into kinetic

energy and so the total energy is conserved. The

positive charge has its greatest potential energy at

point , near the positive plate. For a negative

charge, its potential energy is greatest near the

negative plate.

Now, it is useful to define the electric potential (or

simply the potential, ) as the electric potential energy

per unit charge. If a positive test charge in an

electric field has electric potential energy at some

point (relative to zero potential energy), the electric

potential at this point is;

From this expression, we can write as;

(6)

Potential is potential energy per unit charge. We

define the potential at any point in an elelctric field as

the potential energy per unit charge associated with

a test charge at that point. Potential energy and

charge are both scalar, so potential is a scalar

quantity.

The potential difference between two points and

(in the case of Figure-1, between and ) is

measurable and given by;

or,

We call and the potential at point and

potential at point , respectively. Thus, the work

done per unit charge by the electric force, when a

charged particle moves from to , is equal to the

potential at minus potential at . Note that the

difference is called the potential of with

respect to . The field is directed from regions of

high potential to regions of low potential. The

magnitude of the electric field is largest in region

where is large. Conversely, the electric field is

zero in regions where is constant. In electric circuits,

the unit of electric potential (and potential difference) is

given by ⁄ or . Potential difference

(since it is measured in volts) is often referred to as

(note that ⁄ ).

(5)

(7)

(8)


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3. Electric Field

The electric field at any point in space is defined as

the force exerted on a positive test charge placed at

that point divided by the magnitude of test charge ;

(9)

Here, is the electrostatic force (or Coulomb force)

exerted on a positive test charge, . It is important to

recall that is in the same direction as . It is assumed

that is so small that it does not change the charge

distribution creating the electric field. The test charge

is so tiny that it exerts no force on the other charges

which created the field. For simple situations involving

a single point charge (a particle having a charge, ),

we can calculate the field . The field at a distance

from the point charge has a magnitude;

(11)

Since is a vector quantity, it should have a direction

as well as a magnitude. The direction of the electric

field produced by any charge distribution is the

direction of the force acting on a test positive charge

placed in the field. As you see from the expression, the

electric field is completely independent of the test

charge, . Note that the field depends only on the

charge which produces the field. If we are given

the electric field at a given point in space, then we

can calculate the force on any charge placed at

that point by writing;

(13)

The electric field lines for a point charge are shown

in the Figure-(2). Here, only a few representative lines

are shown. For a single positive point charge, the lines

point radially outward from the charge (Figure-2a) and

for a negative point charge, they point radially inward

toward the charge (Figure-2b). Their density (that is,

their closeness in any region is proportional to the

intensity of the field in that region). Note that nearer the

charge, where the electric field is greater, the electric

field lines are closer together. This is an important

property of electric field lines. Since the electric field

can have one and only one direction at any point in

space, no two electric field lines can pass through the

same point. That is, the electric field lines do not

intersect.

⁄

(10)

(Single Point Charge) (12)

(a)

(b)

Figure-2: Electric field lines of a single positive point charge

(a) and the lines of a single negative point charge (b). The

electric field is stronger where the field lines are closer

together.


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The electric potential at a distance from a single

point charge can be derived directly from the

equation;

∫ (14)

The field is directed radially outward from a positive

charge (inward if ). Figure-(3) shows some of the

electric field lines in a plane containing a single positive

charge. We can take the integral along a straight field

line from point (a distance from ) to a point

(a distance from ). Then, will be parallel to

and . So;

∫

(15)

The electric field due to a single point charge has a

magnitude;

or,

where

⁄ .

Using this expression, we get;

If we choose the potential to be zero at infinity1 (that is,

let at ), then the electric potential at a

distance from a single point charge will be;

This expression for potential implies that is a

constant if is constant. Therefore, equipotential

surfaces (that is, a surface with a constant value of

potential at all points on the surface) of a single point

charge are concentric spherical surfaces centered at

the charge. The potential near a positive charge is

large and it decreases toward zero at very large

distances. However, for a negative charge the

potential is negative and increases toward zero at large

distances. We will deal with the concept of

equipotential surfaces later.

1 Note that we let point be at distance and point

be at infinity. Then, we choose the potential to be zero at infinite distance from the charge.

4. Electric Potential Due to Point Charges

Figure-3: Calculating the electric potential by integrating

for a single point charge.

(16)

(17)

∫

(18)

(

) (19)

(

) (20)

[

] (21)


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5. Relation between Electric Potential and

Electric Field

The difference in potential energy between any two

points in space and is given by;

∫

(22)

This is the relation between a conservative force and

the potential energy associated with that force. Here,

is an infinitesimal increment of displacement. So,

the integral is taken along any path in space from point

to point . Remember that a conservative force is

one for which the work done by the force on a moving

object from one position to another depends only the

two positions and not on the path taken. For example,

the force of gravity is a conservative force. For the

electrical case, we are interested in the potential

difference;

⁄ (23)

As mentioned previously, the electric field at any

point in space is defined to be the ratio of the Coulomb

force to the test charge;

where is the electrostatic force (or Coulomb force)

exerted on a positive test charge . In defining the

electric field, we specify that the test charge is so

small that it does not alter the charge distribution

creating the electric field.

Solving for from these expressions gives;

(25)

∫

(26)

∫

(27)

This is the general relation between electric field, and

potential difference, . In the Figure-(1), for example,

a path parallel to electric field lines from point at

the positive plate to point at the negative plate gives

us;

∫

(29)

Since and are in the same direction at each point,

we can write the potential difference as;

∫

(30)

(31)

Here, is distance parallel to the field lines between

points and . Note that this equation is true only if

the electric field is uniform. The units for electric field

intensity can be written as volts per meter ( ⁄ ) as

well as per Coulomb ( ).

An electric field line is an imaginary line or curve

drawn through a region of space. The direction of the

electric field at any point is tangent to the field line

through that point. Electric field lines show the

direction of at each point and their spacing gives an

idea of the magnitude of the electric field . Where the

electric field is strong, we draw field lines bunched

closely together. Conversely, where is weaker, they

are farther apart. It is also useful to know that two field

lines never intersect one another (that is, only one

field line can pass through each point of the field.). If

they did, the intersection would be a point at which

electric field has two directions. That is to say; the

force on a test charge would have two directions!.

(24)

∫

(28)


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Figure-4: Electric field generated between two oppositely

charged parallel plates.

Consider a system of two metal plates with opposite

charges on them, as shown in the Figure-(4). In

electrostatic equilibrium, the electric field between

the plates (conductors) will be uniform in strength and

direction, except near the edges. The excess charges

distribute themselves uniformly, producing field lines

that are uniformly spaced and perpendicular to the

surfaces. The plates are charged to produce a

potential difference of . The separation between the

plates is . With this information, we can

determine the magnitude of the uniform electric field in

the space between the plates.

⁄

To calculate the magnitude of , assumed uniform, we

apply ⁄ . From this, the electric field magnitude

is ⁄ ⁄ .


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As explained, electric potential is described as

electric potential energy per unit charge. The electric

potential difference between any two points in space is

defined as the difference in potential energy of a test

charge placed at those two points, divided by the

charge, . That is, ⁄ . The electric

potential can be represented graphically by drawing

equipotential lines, or in three dimensions,

equipotential surfaces2. Remind that an equipotential

surface is one on which all points are at the same

potential. This means that the potential difference

between any two points on the surface must be

zero (that is, ).

2 An equipotential line or surface is all at the same

potential and is perpendicular to the electric field at all points.

The equipotential surface is always perpendicular to

the electric field at any point. On a surface where is

constant such that , so we must have either

, in the expression ∫ or,

where is the angle between and

vectors. Therefore, in a region where is not zero, the

path along an equipotential must have ,

meaning and the field is perpendicular to

the equipotential.

Equipotential surfaces (also called equipotential lines

in two-dimensional drawings) are a very useful method

to visualize the electric field and how it varies in

space. Equipotential surfaces are always perpendicular

to the direction of the electric field. In other words,

electric field lines and equipotential surfaces are

mutually perpendicular. This property follows from the

relationship between and . This fact helps us locate

the equipotential surfaces (equipotential lines) and

field lines for a graphical representation. It is

obvious that all points having the same potential will

define an equipotential surface. Also you know that

electric field lines and equipotential surfaces are

always perpendicular. Thus, an imaginary filed line can

be constructed through each of the successive

equipotential surfaces while maintaining the

perpendicularity. This will define a field line through

the electric field.

A basic geometry for the visualization of an electric

field (a field line) is that of a parallel plate capacitor

(see Figure-5). It has two parallel plates each carrying

an equal and opposite electrostatic charge. Between

the plates there will be an electric field (that is, a region

in space where electric forces are experienced). The

equipotential surfaces are parallel planes with

perpendicular field lines. As the example of a parallel

plate capacitor, a few of the equipotential lines are

drawn (dashed lines) for the electric field lines between

two parallel plates at a potential difference of . The

negative plate is chosen to be zero volts and the

potential of each equipotential line is indicated.

6. Equipotential Surfaces

Figure-5: Equipotential lines (dashed lines) between two

oppositely charged parallel metal plates. The equipotential

lines (planes parallel to the metal plates) are perpendicular to

the electric field lines. Note that points toward lower

values of .


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By definition, the electric field of a point charge always

points away from a positive charge but toward a

negative charge. To visualize the electric field, we draw

a series of lines to indicate the direction of the electric

field at various points in space. These electric field

lines are sometimes called lines of force3. They are

drawn so that they indicate the direction of the force

due to the given field on a positive test charge. That

is, the direction of the electric field is the direction of

the force that the test charge experiences. The electric

field can therefore be mapped graphically by lines of

force.

For a simple case of a positive charge, the electric field

lines is directed radially outward, as shown in the

Figure-(6a), because a positively charged test particle

would be repelled radially. The field lines point radially

outward from the charge. The field lines in the plane

of the charge are represented by the by straight lines

and the intersections of the equipotential surfaces

(dashed lines) with this plane (that is, cross sections of

these surfaces) are shown as dashed lines. The actual

equipotential surfaces are three-dimensional. At each

crossing of an equipotential and a field line, the two are

perpendicular since equipotential lines (dashed) are

always perpendicular to the electric field lines.

3 Electric field lines are represented by the lines of

force drawn to follow the direction of the field. These lines are always perpendicular to the equipotential surfaces.

For the case of a negative charge, the force lines

(lines of force) are radially directed inward toward the

negative charge, as a positively charged test particle

would be attracted radially (see Figure-6b).

We can draw the lines so that the number of lines

starting on a positive charge or ending on a negative

charge is proportional to the magnitude of the point

charge. Notice that nearer the point charge, where the

electric field is greater, the lines are closer together. In

other words, the closer together the lines are, the

stronger the electric field in that region.

In general;

Field lines help us visualize electric fields.

The potential at various points in an electric field

can be represented graphically by equipotential

surfaces (or, equipotential lines in two-dimensional

drawings).

Electric field lines and equipotential surfaces are

mutually perpendicular.

We can use a digital (voltmeter) and two

probes (for example, two metal rods) to measure the

potential difference between the two probes. By

placing the probes (connected to the terminals of the

voltmeter) in various positions in an electric field, we

can read the potential differences between the two

positions of the probes. Equipotential surfaces can be

determined by leaving one probe at a fixed position

and then moving the other probe. Whenever the

voltmeter reads zero, the moving probe is at the same

potential as the non-moving probe. That is, the

potential difference between the two probes is zero.

From these considerations, we can map the electric

field from the equipotential lines. On an equipotential

surface where is constant, so . This implies

that the potential remains constant along a path that

is perpendicular to the force lines. Such a path that has

the same value of potential at all points on it is called

an equipotential line in two dimensions, and an

equipotential surface in three dimensions. The field

lines are always perpendicular to the equipotential.

(a) (b)

Figure-6: Electric field lines and equipotential surfaces for a

single positive point charge (a) and a single negative point

charge (b). The field due to a positive charge points

away from the charge, whereas due to a negative charge

points toward that charge.


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As you know, the electric field due to a positive point

charge is visualized by straight lines originating from

the source charge and that due to negative charge by

straight lines terminating at that charge. In the case of

a positive point charge, the electric field is directed

radially outward (Figure-7). Since the equipotential

surfaces must be perpendicular to the lines of the

electric field, they will be spherical in shape, centered

on the point charge (that is, on a given equipotential

surface, the potential has the same value at every

point). Note that different spheres correspond to

different values of . However, the electric field

magnitude needs not to be same (constant) at all

points on the equipotential surface.

In regions where the magnitude of is large, the

equipotential surfaces are close together.

Conversely, in regions where the field is weaker,

the equipotential surfaces are farther apart. This

happens at larger radii, as illustrated in Figure-(7).

The equipotential surface with the largest potential is

closest to the positive charge. As an example, consider

a positive point charge . Assume that

the equipotential surfaces (or lines in a plane

containing the charge) correspond to ,

, . Now, we can sketch the

equipotential surfaces. Recall that the electric potential

depends on the distance from the charge;

From this expression, we have;

For ,

Similarly, for , we get and for

, .

As mentioned earlier, an equipotential surface is a

surface on which the potential has the same value at

every point. Electric field lines and equipotential

surfaces are always mutually perpendicular. In two

dimensional drawings, it is convenient to connect

points of equal potential with lines (these lines are

called equipotential lines).

At a point where a FIELD LINE crosses an

equipotential surface, the two are perpendicular.

For the special case of uniform electric field, in which

the field lines are straight, parallel and equally spaced,

the equipotential surfaces will be parallel planes

perpendicular to the field lines. In other words, for a

uniform electric field, the equipotential surfaces are

parallel planes at right angles to the direction of electric

field.

Figure-7: Electric field lines and equipotential surfaces for a

point charge. The equipotential surfaces around a point

charge are spheres. The circles are projections of the

spherical surfaces onto the plane of the drawing. If you

move in the direction of , electric potential decreases. If

you move in the direction opposite , increases.

[

] (32)

(

) (33)

(

) (34)


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In an electric field produced by a given charge

distribution, there will be many points that have the

same potential. These points are called equipotential

points. If one locates all the equipotential points and

then joins them, one gets an equipotential line. All

points lying on an equipotential line will have the same

potential. The equipotential lines of a given charge

distribution should be perpendicular to the electric field

lines.

A drawing of the electric field lines and equipotential

surfaces of two equal and opposite charges (two

unlike charges) is shown in the Figure-(8). The electric

field of two unlike charges is stronger between the

charges. In that region, the fields from each charge are

in the same direction, so their strengths add. At very

large distances, the field of two unlike charges looks

like that of a smaller single charge. The equipotential

lines are drawn by making them perpendicular to the

electric field lines, if those are known. The electric field

lines are curved in this case and are directed from the

positive charge to the negative charge. The direction

of the electric field at any point is tangent to the field

line at that point. Note that the potential is greatest near

the positive charge and least near the negative charge.

Conversely, if the equipotential lines are known, the

electric field lines can be drawn by making them

perpendicular to the equipotential lines.

Figure-(9) shows the electric field lines for two equal

positive charges. The electric field is weaker between

two same charges, as shown by the lines being farther

apart in that region. This is because the fields from

each charge exert opposing forces on any charge

placed between them. At a great distance from two

same charges, the field becomes identical to the field

from a single, larger charge.

The field lines provide a graphical representation of

the electric fields. So, we can use electric field lines to

visualize and analyze electric fields. At any point on a

field line, the tangent to the line is in the direction of

at that point. In conclusion, it can be said that the

potential at various points in an electric field can be

represented graphically by equipotential surfaces (in

two-dimensions the equipotential surfaces are

equipotential lines);

Graphical representations can be constructed by

drawing equipotential surfaces and field lines.

An equipotential surface is everywhere

perpendicular to the electric field lines (lines of

force) that intersect it. However, electric field lines

never intersect one another. This fact allows us to

use the equipotential surfaces to sketch the

electric field lines.

(a)

Figure-8: Electric field lines due to two equal charges of

opposite sign. Equipotential lines (dashed lines) are always

perpendicular to the electric field lines for two equal but

oppositely charged particles.

Figure-9: Electric field lines and equipotential lines of two

positive equal (same) charges. Lines of force (electric field

lines) are shown as solid lines and arrows. Equipotential

lines are shown as dashed lines.


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In this chapter, we will discuss some properties of

conductors. Conductors contain free charges that

move easily. When there is no net motion of charge

within a conductor, the conductor is said to be in

electrostatic equilibrium. The electric field is zero

everywhere inside the conductor, whether it is solid or

hollow. If the field were not zero, free electrons in the

conductor would experience an electric force ( )

and would accelerate due to this force. This motion of

electrons would mean the conductor is not in

electrostatic equilibrium. Thus, the existence of

electrostatic equilibrium is consistent only with zero

field in the conductor.

We can investigate how this zero field is achieved. Let

us consider a conductor in the form of a slab, as shown

in the Figure-(10). Just before the external field is

applied, free electrons are uniformly distributed

throughout the conductor. When an external field is

applied, the free electrons accelerate, causing negative

charge to accumulate on one side (left surface). The

movement of electrons to one side results in a plane of

positive charge distribution on the right surface.

For a thin flat conductor, the charge accumulates on

the outer surfaces only. These surfaces (planes) of

charge create an additional electric field inside the

conductor that opposes the applied external field. As

the electrons move, the surface charge densities on the

left and right surfaces increase until the magnitude of

the internal field equals that of the external electric

field. This process results in a net field of zero inside

the conductor.

The field must be perpendicular to the conductor’s

surface from the condition of the electrostatic

equilibrium. If the field vector had a component

parallel to the conductor's surface, free electrons would

experience an electric force and move along the

surface. In such a situation, the conductor would not be

in equilibrium. Thus, the electric field at a point just

outside a charged conductor is perpendicular to the

surface (that is, the electric field vector must be

perpendicular to the surface).

7. Electric Fields and Conductors

Figure-10: A slab conductor in an external electric field. The

induced charges on the two surfaces of the conductor

produce an electric field that opposes the external field,

giving a net (resultant) field of zero inside the slab.


15

Now, suppose that a positive charge is surrounded

by an isolated uncharged metal conductor whose

shape is a spherical shell (see Figure-11). There can

be no field within the metal, so the lines leaving the

central positive charge must end on negative charges

on the inner surface of the metal. Thus an equal

amount of negative charge ( ) will be induced on the

inner surface of the spherical shell.

Since the shell is neutral, a positive charge of the same

magnitude ( ) must exist on the outer surface of the

shell. Therefore, although no field exists in the metal

itself, an electric field exists outside of it. There can be

no electric field within a conductor in the static case, for

otherwise the free electrons would feel a force and so

would move. In fact, the entire volume of a conductor

must be entirely at the same potential in the static

case, and the surface of a conductor is then an

equipotential surface4. We know that the field

everywhere inside the conductor, otherwise, charges

would move. It flows that at any point just inside the

surface the component of tangent to the surface is

zero.

4 The surface of a conductor is an equipotential

surface and electric field lines are always normal to the surface.

Some properties of a conductor in electrostatic

equilibrium can be summarized as follows;

1. The electric field is zero inside a conductor.

2. Just outside a conductor, the electric field lines are

perpendicular to its surface, ending or beginning on

charges on the surface.

3. Any excess charge resides entirely on the surface

of a conductor that is, if a conductor in equilibrium

carries a net charge, the charge resides on the

conductor's outer surface. Outside the conductor,

the field is exactly the same as if the conductor

were replaced by a point charge at its center equal

to the excess charge.

4. In the static situation that is, when the charges

are at rest, the surface of any charged conductor is

always an equipotential surface; the electric

potential is constant inside the conductor and is

equal to the potential at the surface of the

conductor.

Figure-11: A charge inside a neutral spherical metal

conductor (shell) induces charge on its surface. Induced

charges appear on the inner and outer surfaces of the

conductor. The electric field within the conductor itself is

zero.


16

An uncharged (neutral) conductor placed in a uniform

electric field is polarized with the most concentrated

charge at its most pointed end. Free charges move

w ithin the conductor, polarizing it , unt il the electric

f ield lines are perpendicular to the surface (that is,

the f ield lines bend so that the external f ield at the

surface is alw ays perpendicular). The external

electric f ield lines end on excess negative charge on

one sect ion of the surface and begin again on

excess posit ive charge on the opposite side. No

electric field exists inside the conductor in static

equilibrium with the external uniform electric field. That

is, in the electrostatic situation, the electric field in the

conductors will be zero, and therefore, all points in on

the conductors will be at the same potential .

Consider a uniform electric field pointing in the positive

direction (Figure-12a). When a neutral conductor of

arbitrary shape is inserted into the external electric field

(Figure-12b), the electric field is distorted and charge

separation occurs on the surface of the conductive

object. Being an equipotential surface, the object

(conductor) is at the potential of the electric field even

though there is no net charge on the surface. Under

electrostatic conditions, the electric f ield inside the

conductor must be zero. No electric f ield exists

inside the conductor.

We can map electric field lines by determining

equipotential lines of two oppositely charged

conductors. Having plotted sufficient equipotential lines

we may then map out the electric field lines which are

normal (perpendicular) everywhere to them. To map

the equipotential lines in a medium between a pair of

charged electrodes and to draw the electric field lines

perpendicular to these lines, the method involves

measuring the potential difference between every two

points in the conductivity medium surrounding two

charged conducting electrodes. The carbon paper

forms the conducting medium or space between the

electrodes. Using a voltmeter, you can measure the

potential difference between any two points in the

medium. If there is no potential difference between any

two points, they must be at the same potential and thus

lie on the same equipotential line.

An equipotential line is a line along which the

electric potential is constant (same). That is, the

potential difference between any two points on an

equipotential line is zero.

Equipotential lines are always perpendicular to

electric field lines. This concept can be used to

draw electric field lines around any type of charge

distribution if the equipotential lines are first

determined. The detailed experimental procedures

are given in the next section.

(a) (b)

Figure-12: A uniform electric field before an uncharged conductor is placed in the field (a). Afterward, the electric field is changed

dramatically, with no electric field inside the conductor (b). Induced charges, which make the electric field inside the conductor

zero, appear on the outside surface of the conductor. There charges affect the electric field outside the conductor.


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1. Plan and draw the layout of two conductive

rings (charged paths) on a graph paper.

1.1. Since these charged paths (charge distributions)

can be any two dimensional shape, such as

circles or dots, they will be referred to as

conductive ink electrodes.

1.2. Draw the rings (two sets of electrodes)

symmetrically along the -axis and -axis on the

paper.

2. Mount the conductive paper (carbon paper) on

the corkboard by using one of the metal pushpins

in each corner of the paper.

Figure-14: Connection of the pin, electrode, wire and

paper on the corkboard.

3. Set up the circuit shown in the Figure-(13).

3.1. Connect the electrodes (two ink electrodes on

the carbon paper) to a power supply by using

connecting wires. Remember that the electrodes

on the carbon paper can be any two-dimensional

shape, such as dots, straight lines or circles.

3.2. Place the terminal of the connecting wire over the

conducting ring electrode and then stick a push

pin through its terminal and the electrode into the

corkboard (see Figure-14).

3.3. The push pin does not act as a conductor. Its

function is only to hold the connecting wire against

the electrode.

8. Experimental Procedures

In this study you will determine and map some of the equipotential lines of a system of oppositely charged conducting rings. The

conducting rings are connected to a power supply. They are drawn by silver conductive ink pen on a black conductive paper

placed on a hard surface. The potential difference between any two points can be measured by touching the probes to the paper at

those points. If two points are at the same potential then these points are called equipotential points.

Figure-13: Experimental circuit for the determination of the

equipotential lines of a system. The conducting rings are

connected to a DC power supply.

To connect wires to the ink electrodes, clean the

terminal on a wire; attach it on an electrode, then

stick a metal push pin through both the terminal

and the electrode into the corkboard. Be sure the

terminal on a wire makes good electrical contact

with the electrode.


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4. Now, check the rings (electrodes) for proper

conductivity. For this procedure;

4.1. Connect one voltmeter probe to a conducting

ring (electrode) near its pushpin.

4.2. Touch the voltmeter’s second probe to several

other points on the same electrode.

4.3. If the ring has been properly drawn, the maximum

potential difference between any two points on the

same electrode will not exceed 1% of the potential

difference between the two electrodes (that is, the

applied power supply voltage).

5. A two-dimensional electric field will be produced

when a voltage is applied across two metal

electrodes that touch the conductive paper.

5.1. Adjust the output voltage of the power supply to

5-6 volts and switch on.

5.2. It is important to keep in mind that if the ground

terminal of the voltmeter is connected to the

negative electrode, and the positive probe to the

other, the volt meter will read the voltage

applied by the power supply.

5.3. To plot the equipotential lines, the ground probe

(one lead) of the voltmeter is touched to the

negative electrode. The potential of this electrode

will be your zero reference potential.

5.4. The second voltmeter probe is touched to any

point on the carbon paper to measure the

potential at that point with respect to the ground

electrode.

6. Now, you are ready to choose six reference

points along the -axis of the paper ( , , , ,

and ).

6.1. Choose these points to be distributed

symmetrically about the origin.

6.2. Touch the probe to one of these points and then

measure and record the potential of this point

with respect to the reference electrode.

. . . . .

6.3. To map an equipotential, move the probe until

the same potential is indicated on the voltmeter.

6.4. Mark the paper at this point with a soft lead

pencil.

6.5. Continue to move the probe, but only in a

direction which maintains the voltmeter at the

same reading. That is;

. . . . .

6.6. Find such ten equipotential points, five above

and five below the -axis.

6.7. Repeat the experiment for the six reference

points you had already chosen on the paper.

6.8. Draw your points on a graph paper representing

the carbon paper.

7. Draw the equipotential (constant voltage) lines

by connecting the equipotential points for each

reference point by a smooth curve.

8. Using the fact that the electric field lines are

perpendicular to the equipotential lines, draw the

electric field lines in the region between two

charged rings.

Recall that electric field lines can never cross.

Field lines must begin on positive charges and

terminate on negative charges for any charge

distribution.

8.1. What are the directions of the electric field lines

for the experimental configuration of two equal

and opposite charge distributions?.

8.2. Are the field lines close together at places where

the field magnitude is large?.


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9. Define equipotential line. How are electric field

lines and equipotential lines drawn relative to

each other?.

10. Will the electric field always be zero at any point

where the electric potential is zero?. Why or

why not?.

11. Will the electric potential always be zero at any

point where the electric field is zero?.

12. By using the carbon paper which already has a

ring, for three of reference points ( , , and ),

investigate the equipotential points in the quarter

in which the ring lies.

12.1. By finding these new equipotential points,

draw the equipotential lines and electric field

lines near the conducting ring on a second

graph paper.

Note that equipotential lines are lines

joining points of the same electric

potential. All electric field lines cross all

equipotential lines perpendicularly.

12.2. How do the equipotential (constant voltage)

lines vary in the presence of the conducting

ring?.

12.3. Draw also the new electric field lines.

Remember that the electric field is zero

inside a conductor. Just outside a

conductor, the electric field lines are

perpendicular to its surface, ending or

beginning on charges on the surface.

12.4. What is true about the electric field just outside

the surface of a conductor?.

12.5. Using the voltmeter probes, verify that the

surface of the conducting ring is indeed an

equipotential surface.


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1. By finding the equipotential points and lines, draw

the electric field lines of two charged rings on the

graph paper. How did you find the direction of the

electric field lines on your graph?.

2. Draw the equipotential lines and electric field lines

near the conducting ring on a second graph

paper.

3. What was the effect of placing the ring on the

equipotential lines and the electric field lines.

4. Describe briefly how you verified that the surface of

the conducting ring is an equipotential surface.

5. Why do we need equipotential lines to draw electric

field lines?.

6. Can two or more equipotential lines intersect each

other?. Explain, briefly.

7. What would happen to the equipotential lines and to

electric field lines when the terminals are reversed?.

9. Laboratory Report

Name: __________________________________

Department: __________________________________

Student No: __________________________________

Date: __________________________________


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Graph-1: Equipotential curves and electric field lines drawn on the graph paper.


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Graph-2: Equipotential lines and electric field lines near the conducting ring on the second graph paper.

equipotential and electric field linesmimoza.marmara.edu.tr/~mdogruel/phys1104/experiment...

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