the electric field...electric field lines (how to visualize electric fields) it is very useful to...

DepartmentofPhysicsandAppliedPhysicsPHYS.1440Lecture2A.Danylov

Lecture 2

Chapter 23

The Electric Field

Physics II

Field?Is it my cute nickname?

Course website:https://sites.uml.edu/andriy-danylov/teaching/physics-ii/


Today we are going to discuss:

Chapter 23:

Section 22.5 Section 23.1 Section 23.2 (skip part about “The electric field of a dipole) Section 23.3 Section 23.4 (skip part about “The Disc of charge”)


Charge induction in an insulator

A neutral atom is polarized by an external charge, forming an electric dipole.

Center of negative charge

negatively charged surface

positively charged surface

electric dipole

F

Demo:rod/paper

ConcepTest Polarization/DipoleX and Y are two uncharged metal spheres on insulating stands, and are in contact with each other. A positively charged rod R is brought close to X as shown in Figure (a).

A) Both X and Y are neutral

B) X is positive and Y is neutral

C) X is neutral and Y is positive

D) X is negative and Y is positive

E) Both X and Y are negative

So we created a dipole.

Sphere Y is now moved away from X, as in Figure (b)What are the final charge states of X and Y?

+ + + + + + + X Y + + + + + + + X Y___

__ ++++

One piece of metalTwo pieces of metal

__

_ ___

++++

+++

+


Demonstrations

A Van de Graff generator (named after its inventor) is a high voltage generator. It basically loads a spherical hollow conductor with static charges which brings the conductor to a very high (or very low) potential.


Idea of an Electric FieldMany forces are “contact forces” (tension, friction, normal, …)

But, the gravitational and electrical (magnetic) forces are “long-range forces” (no contact is required). So, the idea of the field is very useful in these cases.

How to define an electric field?


The Electric Field (definition)How to define an electric field of a charge

What is “not good” about using Coulomb’s law to define a field?

Source of a field

QThe force depends on your probe charge q. Let’s remove it:

1) A probe must be positive (convention) 2) A probe must be small so it wouldn’t

disturb the system created the field

Probe charge

The units of the electric field are N/C. The magnitude E of the electric field is called the electric field strength.

q=1C

F=1N

q=5C

F=5N

Using Coulomb’s law?

q


The Electric Field of a Point Charge

The electric field at a distance r from a point charge Q

Let’s find an electric field at a distance r from a point charge q is:

Q

qprobe=


Electric field lines (how to visualize electric fields)

It is very useful to picture an electric field using electric field lines. This concept was introduced by M. Faraday as an aid in visualizing electric fields.

The lines emanate from a positive charge and terminate on a negative one.

Mapping of an electric field


Electric field lines (two charges/dipole)Field lines of two equal but opposite charges

Smaller density of lines,the field is weaker

The field is stronger

1) The electric field vector is tangent to the field line at that point2) The lines emanate from a positive charge and terminate on a negative one.

For the upper charge, the E field vector at the center of the square points toward that charge. For the lower charge, the same thing is true. Then the vector sum of these two Efield vectors points to the left.

Whatistheelectricfieldat

thecenterofthesquare? DC

B A

-2 C

-2 C

E) E = 0

ConcepTest Electric Field

Follow-up: What if the lower charge were +2 C? What if both charges were +2 C?

E

E

-2 C

-2 CProbe charge


Once E is known, it is easy to get F

A charged particle with charge q at a point in space where the electric field is E experiences an electric force:

The force on a negative charge is opposite the direction of E.

EF

F

If q is positive, the force on the particle is in the direction of E.

(Uniform Electric Field)

Since the 4 C charge feels a force, there mustbe an electric field present, with magnitude:

E = F / q = 12 N / 4 C = 3 N/COnce the 4 C charge is replaced with a 6 Ccharge, this new charge will feel a force of:

F = q E = (6 C)(3 N/C) = 18 N

Q

A) 12 N

B) 8 N

C) 24 N

D) no force

E) 18 N

ConcepTest Uniform Electric Field

Follow-up: What if the charge is placed at a different position in the field?

Inauniformelectricfieldinemptyspace,a4Cchargeisplacedanditfeelsanelectricforceof12N.Ifthischargeisremovedanda6Cchargeisplacedatthatpointinstead,whatforcewillitfeel?

ConcepTest Electric Field Lines

Whatarethesignsofthechargeswhoseelectricfieldsareshownatright?

A)

B)

C)

D)

E) no way to tell

Electric field lines originate on positive charges and terminate on negative charges.

‐ +


Conclusions

• Electric field arrows show the direction of the force on a small positive probe charge

• Field lines begin at positive charges and end at negative charges

• Field strength is proportional to line density• Direction of the electric field at a point is tangent to the

electric field line at that point• Field lines are continuous and never cross

It’s all about me


Thank you

the electric field...electric field lines (how to visualize electric fields) it is very useful to...

Documents