1. Three parallel plates with area A and separation d are shown below. The middl

Question

1. Three parallel plates with area A and separation d are shown below. The middle plate has a charge -Q, and the bottom plate and top plates are grounded (at V=0). Find:

a) Charge on top and bottom plates.

b) Electric field at all points in space.

c) The potential of the middle plate

2. Refer to the circuit shown below.

a) Why is the following statement true? Statement: After the switch is closed, bulb A glows less brightly than before.

b) Why is the following statement false? Statement: In the situation shown, Vb - Va = 12V, the current is 2A to the right.

c) Why is the following statement true? Statement; The total stored energy of a conducting sphere of radius R, carrying charge Q, increases as R is decreased.

Explanation / Answer

(A) top and bottom plates are grounded so

Q = 0

(B) E = Q / 2 e0

(C) V= Q d / 2 e0

2. initially, IA = V / (RA + R)

after switch is closed,

Req = R + RA RB / (RA + RB)

= (R RA + R RB + RA RB) / (RA + RB)

IA = (V / Req) (RB) / (RA + RB)

= V RB / (R RA + R RB + RA RB)

= V / (R RA + R + RA)

so IA_final < IA _initial

True

(B) A and B are in parallel
  
So Va = Vb

hence Va - Vb= 0

False

(C) E = K Q / R^2

and energy stored = (energy denisty) (volume)

= e0 E^2 (4 pi R^3 / 3)

= k 4 pi e0 Q^2 / 3 R

and k =1 /4 pi e0

= Q^2 / (3 R)

R- > decreases then energy stored-> increases

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