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51Monday, January 12, 2009

PHYS 1030 this week:

Experiment 1: Equipotential Lines

52Monday, January 12, 2009

• Conductor contains charges that are free

to move (electrons)

• At equilibrium, the charges are at rest

Electrical Conductor

E = 0

! there can be no electric field inside the conductor, otherwise the

charges would be moving under the influence of the field and would

not be in equilibrium.

The electric fields due to

the rod and the charges on

the surface cancel each

other out inside the

conductor

53Monday, January 12, 2009

E = 0

The extra electrons are pushed to the surface of the conductor by the

repulsive Coulomb forces between them.

As the electrons end up at equilibrium (i.e. at rest) there can be no electric

field inside the conductor, otherwise the electrons would still be moving...

Put some extra electron charges inside the conductor

Electrical Conductor

54Monday, January 12, 2009

E =q

!0A

Coulomb constant, k =1

4!"0

Uniform field inside a parallel plate capacitor

+q -q

Area A

!E

Uniform

spacing of field

lines means

constant

electric field

55Monday, January 12, 2009

At equilibrium, electric field lines are made to hit the conductor at

right angles – charges have moved around the surface until they

reached an equilibrium in which there is no longer a field parallel to the

surface to move them further.

Uniform spacing of field lines

means constant electric field

E = 0

Distortion of field lines due to charges on surface of conductor

–e E=0

56Monday, January 12, 2009

Equipotential SurfaceAs the electric field lines are at

right angles to the conducting

surface, no work is done in moving

an electron charge around the

surface

! the electron has constant

potential energy on the surface

! the surface is an “equipotential

surface” (more in chapter 19)

– equipotential surfaces are at

right angles to electric field lines

Electric potentials are measured in

volts (V).

–eE = 0

!E

57Monday, January 12, 2009

Experiment 1 : Equipotential Lines

Sketch out equipotential lines by using a voltmeter to find

places that lie at the same potential (voltage).

– one probe of the voltmeter is fixed in position, the other is

moved around to locate points that give the same voltage

reading on the voltmeter.

– all of the points giving the same reading on the voltmeter lie

on an equipotential line.

Electric field lines are sketched in so that they are always at

right angles to the equipotential lines.

58Monday, January 12, 2009

Equipotentials and electric field

V1 volts

V2 volts

90º

90º 90º

90º

59Monday, January 12, 2009

Equipotentials and Field Lines

V = 0

E

E

V

V

60Monday, January 12, 2009

E = 0

E = 0

Scooping out material where there is no electric field

results in a cavity with no electric field

Interior of the cavity is shielded from outside fields – basis of “Faraday cage”

– example, shielding of electronic circuits (in a closed metal box) from stray

electric fields61Monday, January 12, 2009

The number of field lines leaving +q is

equal to the number hitting the inner

surface of the conductor...

! there must be an induced charge

of –q on the inner surface of the

conductor (the field lines point

toward the inner surface, so the

induced charge must be negative).

As the outer surface has a charge +q, it must have the same number of lines

leaving the surface

! from the outside, the conductor has no effect on the electric field.

–q

+q

As the conductor is electrically neutral (has zero

net charge), there must also be an induced charge

+q on the outer surface of the conductor.

E = 0

Charge +q placed inside an

uncharged hollow conductor

62Monday, January 12, 2009

Clicker Question

A metal sphere with a hollow centre has a charge of +2q, initially all

on the outer surface.

An additional charge +q is placed in the hollow centre of the sphere.

The charge on the outer surface of the sphere becomes:

A) -q

B) 0

C) +q

D) +2q

E) +3q+q Metal sphere

+2q

Hints: The number of field lines

is proportional to charge.

What is the charge on the inner surface of the conductor?

Charge is conserved.

63Monday, January 12, 2009

Inside an Electrical Conductor

Charges (electrons) are free to move, so that:

• forces between charges push charges to the surface of the conductor

• charges move around the surface until they come to equilibrium

• as the charges are at rest, there must be zero force acting on them

! the electric field inside the conductor must be zero

• as the charges are at equilibrium, electric field lines

must hit the conductor at right angles, otherwise

charges would be moved around the surface

! no work is done in moving charges around the surface

! charges on the surface must have constant potential energy

! the surface of the conductor is an “equipotential”

E = 0

e-

64Monday, January 12, 2009

Inside an Electrical Insulator

Electric charges cannot move, so:

→ charges do not move around to reduce the electric field to zero

→ an electric field can exist inside an insulator

65Monday, January 12, 2009

Prob. 18.24: There are four charges, each of magnitude 2 !C. Two

are positive and two are negative.

The charges are fixed to the corners of a 0.3 m square, one to a

corner, in such a way that the net force on any charge is directed to

the centre of the square.

Find the magnitude of the electrostatic force experienced by any

charge.

Work out how to arrange the four charges so that the net force on

each is toward the centre of the square –"implies there must be

some symmetry in the arrangement of charges.

66Monday, January 12, 2009

18.45: Two point charges of the same magnitude but opposite signs

are fixed to either end of the base of an isosceles triangle. The

electric field at the midpoint M between the charges has a magnitude

EM. The field at point P has magnitude EP.

The ratio of these two field magnitudes is EM/EP = 9.0. Find the angle

αin the diagram.

LL

dd

cos ! =d

L

67Monday, January 12, 2009

Prob. 18.19/67: Two small spheres are mounted on identical horizontal

springs and rest on a frictionless table.

When the spheres are uncharged, the spacing between them is 0.05 m,

and the springs are unstrained.

When each sphere has a charge of +1.6 !C, the spacing doubles.

Determine the spring constant, ks, of the springs.

68Monday, January 12, 2009