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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

#### 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

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#### 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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