A spherical conducting shell of inner radius r1 and outerradius r2 has a charge Q.
(a) A charge q is placed at the centre of the shell.What is the surface charge density on the inner and outer surfaces ofthe shell?
(b) Is the electric field inside a cavity (with no charge)zero, even if the shell is not spherical, but has any irregularshape? Explain.
A spherical conducting shell of inner radius r1 and outerradius r2 has a charge Q.
(a) A charge q is placed at the centre of the shell.What is the surface charge density on the inner and outer surfaces ofthe shell?
(b) Is the electric field inside a cavity (with no charge)zero, even if the shell is not spherical, but has any irregularshape? Explain.
(a) Charge placed at the centre of a shell is +q.Hence, a charge of magnitude −q will be induced to theinner surface of the shell. Therefore, total charge on the innersurface of the shell is −q.
Surfacecharge density at the inner surface of the shell is given by therelation,
Acharge of +q is induced on the outer surface of the shell. Acharge of magnitude Q is placed on the outer surface of theshell. Therefore, total charge on the outer surface of the shell is Q+ q. Surface charge density at the outer surface of the shell,
(b) Yes
Theelectric field intensity inside a cavity is zero, even if the shellis not spherical and has any irregular shape. Take a closed loop suchthat a part of it is inside the cavity along a field line while therest is inside the conductor. Net work done by the field in carryinga test charge over a closed loop is zero because the field inside theconductor is zero. Hence, electric field is zero, whatever is theshape.
(a) Charge placed at the centre of a shell is +q.Hence, a charge of magnitude −q will be induced to theinner surface of the shell. Therefore, total charge on the innersurface of the shell is −q.
Surfacecharge density at the inner surface of the shell is given by therelation,
Acharge of +q is induced on the outer surface of the shell. Acharge of magnitude Q is placed on the outer surface of theshell. Therefore, total charge on the outer surface of the shell is Q+ q. Surface charge density at the outer surface of the shell,
(b) Yes
Theelectric field intensity inside a cavity is zero, even if the shellis not spherical and has any irregular shape. Take a closed loop suchthat a part of it is inside the cavity along a field line while therest is inside the conductor. Net work done by the field in carryinga test charge over a closed loop is zero because the field inside theconductor is zero. Hence, electric field is zero, whatever is theshape.
