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A Spherical Conducting Shell of Inner Radius R1 and Outer Radius R2 Has a Charge Q. - CBSE (Science) Class 12 - Physics

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Question

A spherical conducting shell of inner radius r1 and outer radius r2 has a charge Q.

(a) A charge is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell?

(b) Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.

Solution

 

(a) Charge placed at the centre of a shell is +q. Hence, a charge of magnitude −q will be induced to the inner surface of the shell. Therefore, total charge on the inner surface of the shell is −q.

Surface charge density at the inner surface of the shell is given by the relation,

`sigma_1="total Charge"/"inner surface area"=-q/(4pir_2^2)`   ...(1)

A charge of +q is induced on the outer surface of the shell. A charge of magnitude Q is placed on the outer surface of the shell. Therefore, total charge on the outer surface of the shell is Q + q. Surface charge density at the outer surface of the shell,

`sigma_2="total Charge"/"outersurface area"=(Q+q)/(4pir_2^2)`  ...(2)

(b) Yes

The electric field intensity inside a cavity is zero, even if the shell is not spherical and has any irregular shape. Take a closed loop such that a part of it is inside the cavity along a field line while the rest is inside the conductor. Net work done by the field in carrying a test charge over a closed loop is zero because the field inside the conductor is zero. Hence, electric field is zero, whatever is the shape

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Physics Textbook for Class 12 (2018 to Current)
Chapter 2: Electrostatic Potential and Capacitance
Q: 15 | Page no. 88
Solution A Spherical Conducting Shell of Inner Radius R1 and Outer Radius R2 Has a Charge Q. Concept: Electrostatics of Conductors.
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