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Chapter 4: Q70P (page 782)

An insulating spherical shell with inner radius 25.0 cm and outer radius 60.0 cm carries a charge of +150.0渭颁uniformly distributed over its outer surface. Point a is at the center of the shell, point b is on the inner surface, and point c is on the outer surface. (a) What will a voltmeter read if it is connected between the following points: (i) a and b; (ii) b and c; (iii) c and infinity; (iv) a and c? (b) Which is at higher potential: (i) a or b; (ii) b or c; (iii) a or c? (c) Which, if any, of the answers would change sign if the charge were -150渭C?

Short Answer

Expert verified
  1. Potential difference between points is
  1. 0V
  2. 0V
  3. 2.25脳106V
  4. 0V
  5. Potential is the same in all the cases.
  6. Sign is negative.

Step by step solution

01

Step 1:

(a) As the enclosed chargeqenforr<ri is zero and the potential is constant and equivalent to the potential at the outer surface.

And as the enclosed charge is zero forri<r<r0and the potential is constant and equal to the outer surface potential.

Therefore for r>r0the enclosed charge is the net charge,

So, the potential is

Vr=KQr

And potential at the surface

Vr0=KQr0

02

Step 2:

So, the potential difference between the points is:

(i) For a and b

Vab=Va-Vb=Vr0-Vr0=0V

(ii) For b and c

Vbc=Vb-Vc=Vr0-Vr0=0V

(iii) For c and infinity

Va鈭�=Va-V鈭�=kQr0-0=9脳109脳150脳10-60.6=2.25脳106V



(iv) For a and c

Vac=Va-Vc=Vr0-Vr0=0V

03

Step 3:

(b) Thus, the Potential will remain the same for (a, b, c) and will be equal to the surface potential.

04

Step 4:

(c) If a charge is changed the electric potential will equal a, b, and c with a negative value.

Thus, the potential at a, b and c will be

-2.25脳106V

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