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Chapter 23Chapter 23Electric FieldsElectric Fields

23.1 Properties of Electric Charges23.1 Properties of Electric Charges

23.3 Coulomb’s Law23.3 Coulomb’s Law

23.4 The Electric Field23.4 The Electric Field

23.6 Electric Field Lines23.6 Electric Field Lines

23.7 Motion of Charged Particles 23.7 Motion of Charged Particles in a Uniform Electric Fieldin a Uniform Electric Field

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23.123.1 Properties of Electric ChargesProperties of Electric Charges• There are two kinds of

electric charges in nature:– Positive – Negative

• Like charges repel one another and Unlike charges attract one another.

• Electric charge is conserved.

• Charge is quantized q=Ne

e = 1.6 x 10-19 CN is some integer

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From Coulomb’s experiments, we can generalize the following properties of the electric force between two stationary charged particles.

The electric force• is inversely proportional to the square of the

separation r between the particles and directed along the line joining them.

• is proportional to the product of the charges q1 and q2 on the two particles.

• is attractive if the charges are of opposite sign and repulsive if the charges have the same sign.

23.323.3 Coulomb’s LawCoulomb’s Law

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• Consider two electric charges: q1 and q2

• The electric force F between these two charges separated by a distance r is given by Coulomb’s Law

• The constant ke is called Coulomb’s constant

0 is the permittivity of free space

• The smallest unit of charge e is the charge on an electron (-e) or a proton (+e) and has a magnitude e = 1.6 x 10-19 C

2

212

00 Nm

C 1085.8 where

4

1

k

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Example 23.1Example 23.1 The Hydrogen AtomThe Hydrogen Atom

The electron and proton of a hydrogen atom are separated (on the average) by a distance of approximately 5.3 x 10-11 m. Find the magnitudes of the electric force.

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• When dealing with Coulomb’s law, you must remember that force is a vector quantity

• The law expressed in vector form for the electric force exerted by a charge q1 on a second charge q2, written F12, is

• where rˆ is a unit vector directed from q1 toward q2

• The electric force exerted by q2 on q1 is equal in magnitude to the force exerted by q1 on q2 and in the opposite direction; that is, F21= -F12.

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• When more than two charges are present, the force between any pair of them is given by Equation

• Therefore, the resultant force on any one of them equals the vector sum of the forces exerted by the various individual charges.

• For example, if four charges are present, then the resultant force exerted by particles 2, 3, and 4 on particle 1 is

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• Double one of the charges– force doubles

• Change sign of one of the charges– force changes direction

• Change sign of both charges– force stays the same

• Double the distance between charges– force four times weaker

• Double both charges– force four times stronger

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ExampleExample::

• Three point charges are aligned along the x axis as shown. Find the electric force at the charge 3nC.

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Example 23.2Example 23.2 Find the Resultant ForceFind the Resultant Force

• Consider three point charges located at the corners of a right triangle, where q1=q3= 5.0μC, q2= 2.0 μC, and a= 0.10 m. Find the resultant force exerted on q3.

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