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Chapter 21: Electric Charge and Electric Field

Sai Iyer

Electric Charge

Gold Leaf Electroscope

Invented by Abraham Bennet in 1787.

Gold leaf electroscope:http://upload.wikimedia.org/wikipedia/commons/d/de/Gold_leaf_electroscope_with_ground_strips.png.

Charged electroscope: http://www.gcsescience.com/Charged-Electroscope.gif .

Animation: http://mw.concord.org/modeler1.3/mirror/electrostatics/electroscope.html

Properties of Electric Charge

There are two kinds of electric charge: positive (+) and negative (-).

Like charges repel each other and unlike charges attract each other.

Charge is conserved.

Charge is quantized. Any observable charge is a multiple of the charge of the electron. Since theobjects we deal with will have many, many electronic charges, we can treat charge as a continuousquantity.

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http://upload.wikimedia.org/wikipedia/commons/d/de/Gold_leaf_electroscope_with_ground_strips.pnghttp://upload.wikimedia.org/wikipedia/commons/d/de/Gold_leaf_electroscope_with_ground_strips.pnghttp://upload.wikimedia.org/wikipedia/commons/d/de/Gold_leaf_electroscope_with_ground_strips.pnghttp://upload.wikimedia.org/wikipedia/commons/d/de/Gold_leaf_electroscope_with_ground_strips.pnghttp://www.gcsescience.com/Charged-Electroscope.gifhttp://www.gcsescience.com/Charged-Electroscope.gifhttp://mw.concord.org/modeler1.3/mirror/electrostatics/electroscope.htmlhttp://mw.concord.org/modeler1.3/mirror/electrostatics/electroscope.htmlhttp://mw.concord.org/modeler1.3/mirror/electrostatics/electroscope.htmlhttp://mw.concord.org/modeler1.3/mirror/electrostatics/electroscope.htmlhttp://www.gcsescience.com/Charged-Electroscope.gifhttp://upload.wikimedia.org/wikipedia/commons/d/de/Gold_leaf_electroscope_with_ground_strips.pnghttp://upload.wikimedia.org/wikipedia/commons/d/de/Gold_leaf_electroscope_with_ground_strips.png

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Phys 212 (SP12) Chapter 21 2

Charges in an Atom

Protons are positively charged, electrons are negatively charged, and neutrons are uncharged.Theelectrons dont combine with the protons due to quantum mechanical effects. The protons dont flyapart from each other due to nuclear forces. (We will study these topics later in the semester.)

The protons charge is equal in magnitude to the electrons charge.

A neutral atom has equal numbers of protons and electrons.

A positive ion has more protons than electrons.

A negative ion has fewer protons than electrons.

Conductors and Insulators

Conductors allow charges to flow freely through them. Most metals are conductors.

Insulators do not permit the free flow of charge. Most non-metals are insulators.

Animation: http://regentsprep.org/Regents/physics/phys03/ainsvscon/default.htm.

Charging by Contact and by Induction

Electric charge can be transferred from one object to another through physical contact, or can beinduced.

Charging gold leaf electroscope by induction: http://en.wikipedia.org/wiki/File:Electroscope_showing_induction.png

When charging by contact, the original body loses some of its charge to the body being charged.

When charging by induction, the original body does not lose any of its charge.

The induced charge is opposite in sign to the inducing charge.
http://regentsprep.org/Regents/physics/phys03/ainsvscon/default.htmhttp://regentsprep.org/Regents/physics/phys03/ainsvscon/default.htmhttp://en.wikipedia.org/wiki/File:Electroscope_showing_induction.pnghttp://en.wikipedia.org/wiki/File:Electroscope_showing_induction.pnghttp://en.wikipedia.org/wiki/File:Electroscope_showing_induction.pnghttp://en.wikipedia.org/wiki/File:Electroscope_showing_induction.pnghttp://regentsprep.org/Regents/physics/phys03/ainsvscon/default.htm

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PolarizationA charged object brought near an uncharged object (even an insulator) produces a separation of charges

in the uncharged object. Since the charges of opposite sign are closer to the charged object, there is a netattraction. This separation of charges is known as polarization.

Coulombs Law

Discovered in 1783.

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Magnitude of the force:

F =1

40

|q1q2|

r2

Charge is measured in coulombs (C).

The magnitude of the electrons charge, e, is 1.602 1019 C.

0 = 8.854 1012 C2/N m2

140 = (107 N s2/C2)c2 9.0 109N m2/C2, where c is the speed of light in vacuum.

See examples 21.1 and 21.2.

The electric force is much stronger than the gravitational force. But since negative and positive chargesare almost exactly balanced in objects, the net electrical force between objects is small.

Coulombs law is strictly valid only for stationary charges. It is approximately true for slowly moving

charges. This is known as the electrostatic approximation.

Principle of Superposition of Forces

The total force due to several charges on a given charge is the vector sum of the forces due to theindividual charges.


Electric Field

Introduced by Faraday.

The force due to a charge q on a small test charge q0 at a distance r is

F0 =1

40

|qq0|

r2

We define the field due to q at the location ofq0 by

E =F0q0

In this view, q produces a field E which acts on q0.

q0 has to be small enough not to disturb the source charge.

Electric Field due to a Point Charge

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Electric field:

E =1

40

q

r2r

The field due to a positive charge points away from it.

The field due to a negative charge points toward it.


Superposition of Electric Fields

The principle of superposition applies to electric fields.

Example:

See example 21.8

Force due to an Electric Field

The force on a point charge q due to an electric field E is given by

F= qE

The force is in the direction of the field for a positive charge q and in the opposite direction for anegative charge q.

Note that E here is not of the form1

40

q

r2runless it is due to another point charge.

See example 21.7. (Review projectile motion from last term.)

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Field due to a Continuous Charge Distribution

We divide the charge distribution into small elements dQ which we can treat as point charges.

E =dE, where dE is the field due to dQ.

See examples 21.9, 21.10, 21.11, 21.12 for important cases.

Electric Field Lines

Electric field lines are imaginary lines that help us visualize the electric field.

A field line is tangent to E at every point.

Field lines are bunched closer together where the field is more intense, and spread farther apart wherethe field is less intense.

Field lines point away from positive charges and point toward negative charges.

Animation: http://www.falstad.com/emstatic/.

Electric Dipole

The magnitude of the electric dipole moment is p = qd and the direction is from the negative chargeto the positive charge.

The torque on the dipole is = pE.

The potential energy of the dipole is U= p E.

http://www.falstad.com/emstatic/http://www.falstad.com/emstatic/http://www.falstad.com/emstatic/

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