Chapter 16 Section 2 Electric force

Objectives

Calculate electric force using Coulomb’s law.

Compare electric force with gravitational force.

Apply the superposition principle to find the resultant force on a charge and to find the position at which the net force on a charge is zero.

Coulomb's Law

Two charges near one another exert a force on one another called the electric force.

Coulomb’s law states that the electric force is proportional to the magnitude of each charge and inversely proportional to the square of the distance between them.

1 22

2

charge 1 charge 2electric force = Coulomb constant

distance

electric C

q qF k

r

Coulomb’s Law

The quantitative expression for the effect of these three variables on electric force is known as Coulomb's law. Coulomb's law states that the electrical force between two charged objects is directly proportional to the product of the quantity of charge on the objects and inversely proportional to the square of the separation distance between the two objects.

Coulomb’s Law

The resultant force on a charge is the vector sum of the individual forces on that charge.

Adding forces this way is an example of the principle of superposition.

When a body is in equilibrium, the net external force acting on that body is zero.

Sample Problem

The Superposition Principle

Consider three point charges at the corners of a triangle, as shown at right, where q1 = 6.00 10–9 C, q2 = –2.00 10–9 C, and q3 = 5.00 10–9 C. Find the magnitude and direction of the resultant force on q3.

solution

The Superposition Principle

1. Define the problem, and identify the known variables.

Given:

q1 = +6.00 10–9 C r2,1 = 3.00 m

q2 = –2.00 10–9 C r3,2 = 4.00 m

q3 = +5.00 10–9 C r3,1 = 5.00 m

= 37.0º

Unknown: F3,tot = ? Diagram:

solution

Tip: According to the superposition principle, the resultant force on the charge q3 is the vector sum of the forces exerted by q1 and q2 on q3. First, find the force exerted on q3 by each, and then add these two forces together vectorially to get the resultant force on q3.

2. Determine the direction of the forces by analyzing the charges.

The force F3,1 is repulsive because q1 and q3 have the same sign.

The force F3,2 is attractive because q2 and q3 have opposite signs.

solution

3. Calculate the magnitudes of the forces with Coulomb’s law.

–9 –9293 1

3,1 22 2

–83,1

–9 –9293 2

3,2 22 2

–93,1

5.00 10 C 6.00 10 CN m 8.99 10

( 3,1) C 5.00 m

1.08 10 N

5.00 10 C 2.00 10 CN m8.99 10

( 3,2) C 4.00m

5.62 10 N

C

C

q qF k

r

F

q qF k

r

F

solution

Find the x and y components of each force.

At this point, the direction each component must be taken into account.

F3,1: Fx = (F3,1)(cos 37.0º) = (1.08 10–8 N)(cos 37.0º)

Fx = 8.63 10–9 N

Fy = (F3,1)(sin 37.0º) = (1.08 10–8 N)(sin 37.0º)

Fy = 6.50 10–9 N

F3,2: Fx = –F3,2 = –5.62 10–9 N

Fy = 0 N

solution

6. Use the Pythagorean theorem to find the magnitude of the resultant force.

2 2 9 2 9 23, , ,

–93,

( ) ( ) (3.01 10 N) (6.50 10 N)

7.16 10 N

tot x tot y tot

tot

F F F

F

solution

Use a suitable trigonometric function to find the direction of the resultant force.

In this case, you can use the inverse tangent function

–9,

–9,

6.50 10 Ntan

3.01 10 N

65.2º

y tot

x tot

F

F

Example

Suppose that two point charges, each with a charge of +1.00 Coulomb are separated by a distance of 1.00 meter. Determine the magnitude of the electrical force of repulsion between them.

solution

Given:Q1 = 1.00 C Q2 = 1.00 Cd = 1.00 m

Find:Felect = ???

Felect = k • Q1 • Q2 / d2 Felect = (9.0 x 109 N•m2/C2) • (1.00 C) • (1.00 C) / (1.00 m)2 Felect = 9.0 x 109 N

The first step of the strategy is the identification and listing of known information in variable form. Here we know the charges of the two objects (Q1 and Q2) and the separation distance between them (d). The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the force. So Felect is the unknown quantity. The results of the first two steps are shown in the table below

Example

Two balloons are charged with an identical quantity and type of charge: -6.25 nC. They are held apart at a separation distance of 61.7 cm. Determine the magnitude of the electrical force of repulsion between them.

solution

The problem states the value of Q1 and Q2. Since these values are expressed in units of nanoCoulombs (nC), the conversion to Coulombs must be made. The problem also states the separation distance (d). Since distance is given in units of centimeters (cm), the conversion to meters must also be made. These conversions are required since the units of charge and distance in the Coulomb's constant are Coulombs and meters. The unknown quantity is the electrical force (F). The results of the first two steps are shown in the table below.

Given:Q1 = -6.25 nC = -6.25 x 10-9 C Q2 = -6.25 nC = -6.25 x 10-9 Cd = 61.7 cm = 0.617 m

Find:Felect = ???

solution

The final step of the strategy involves substituting known values into the Coulomb's law equation and using proper algebraic steps to solve for the unknown information. This substitution and algebra is shown below.

Felect = k • Q1 • Q2 / d2 Felect = (9.0 x 109 N•m2/C2) • (6.25 x 10-9 C) • (6.25 x 10-9 C) / (0.617 m)2

Felect = 9.23 x 10-7 N

Example

Two balloons with charges of +3.37 µC and -8.21 µC attract each other with a force of 0.0626 Newton. Determine the separation distance between the two balloons.

solution

Given:Q1 = +3.37 µC = +3.37 x 10-6 C Q2 = -8.21 µC = -8.21 x 10-6 CFelect = -0.0626 N (use a - force value since it is attractive)

Find:d = ???

The problem states the value of Q1 and Q2. Since these values are in units of microCoulombs (µC), the conversion to Coulombs will be made. The problem also states the electrical force (F). The unknown quantity is the separation distance (d). The results of the first two steps are shown in the table below

Felect = k • Q1 • Q2 / d2 d2 • Felect = k • Q1 • Q2

d2 = k • Q1 • Q2 / Felect d = SQRT(k • Q1 • Q2) / Felect d = SQRT [(9.0 x 109 N•m2/C2) • (-8.21 x 10-6 C) • (+3.37 x 10-6 C) / (-0.0626 N)]d = Sqrt [ +3.98 m2 ]d = +1.99 m

Coulomb’s Law

The Coulomb force is a field force.

A field force is a force that is exerted by one object on another even though there is no physical contact between the two objects.

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closure

Today we learned about electric force and coulomb’s law

Next class we are going to learn about electric fields