Review

Coulomb’s Law

221

rQQkF

Units of Charge

1 Coulomb (C)

229229 /100.9/10988.8 CmNCmNk

Direction of the electric force is always along the line joining the two objects.

Direction of the force depends on whether the charges have the same sign or opposite sign.

Coulomb’s Law in terms of 0, permittivity of free space.

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1

22120

221

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mNCk

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Conceptual Example

Two positive point charges Q1=50 C and Q2=1 C, are separated by a distance l. Which is larger in magnitude, the force that exerts on Q1 exerts on Q2, or the force that Q2 exerts on Q1?

The Electric Field

The electric field E at a point in space is defined as an electric force F, acting on a positive test charge q divided by the magnitude of the test charge

qFE

204

1rQE

Units of Electric Field

1 N/C

Field Lines

1. At every point of electric field line, electric field E is tangent to this line. No two field lines can cross!

2. The line must begin at positive charge and terminate on the negative one unless go to infinity.

3. The number of line per unit area is proportional to the magnitude of electric field.

Electric Fields and Conductors

Important: electric field inside of good conductor is zero!!!!

Important: any net charge on a good conductor distributes itself on the surface!!!!

Electric field is always perpendicular to the surface of conductor:

q Q

P

dd

Is it possible to place a charge at point Q such that the electric field produced at point P by the two charges will be add to zero?

Electric Potential and Electric Energy

It’s useful to define the electric potential (or simply the potential) as a potential energy per unit charge:

qPEV a

a

Units of Electric Potential

1 V = 1 J/C

dVE ba

Important: this simple formula for E may be used only for uniform field!!!!

Equipotential Lines

The equipotential surface must be perpendicular to the surface.

Important: the surface of a good conductor is always an equipotential surface!!!!

Electric Potential Due to Point Charges

rQV

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Work to Force Two Positive Charges Close Together

What minimum work is required by an external force to bring a charge q=3.00 C from a great distance away to a point 0.5 m from a charge Q=20C?

Capacitance

Q = CV

The constant of proportionality, C , in the last relation is called the capacitance of the capacitor.

Important: the capacitance C is a constant for a given capacitor; it does not depend on charge Q or voltage V.

Capacitance of a Parallel-PlateCapacitor

dAC 0

dAKC 0

Energy Stored in Capacitor

CQCVQVU

22

21

21

21

When such a circuit is formed, charge can flow through the wires of the circuit, from one terminal of the battery to the other. A flow of charge such as this is called as electric current.

tQI

Units of Current

1 Ampere (A) = 1 C /1 s

Important: Current is not a vector, it’s a scalar!!!!

Definition of Resistance

I=V/R

Ohm’s Law

The current through a metal conductor is proportional to the applied voltage.

Resistivity

ALR

Effect of Temperature

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– temperature coefficient of resistivity is positive for metals and negative for semiconductors.

Electric Power

RVRIIVP

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ftRIRIP

ftR

VRVI

ftVV

2sin

2sin

2sin

220

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Average Power

RVP

RIP

20

20

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Root-Mean-Square Values (RMS)

002

002

707.02

707.02

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rms

rms