NCERT Class XII Chapter
Electrostatic Potential and Capacitance
Questions With Solutions
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Question : 15
Total: 37
A spherical conducting shell of inner radius r 1 r 2
(a) A charge q 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.
(a) A charge q 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) Surface charge density on the inner surface of shell is
σ in −
and on the outer surface of shell is
σ out
(b) The electric flux linked with any closed surface S inside the conductor is zero as electric field inside conductor is zero.
So, by Gauss’s theorem net charge enclosed by closed surface S is also zero i.e.,q net
So, if there is no charge inside the cavity, then there cannot be any charge on the inner surface of the shell and hence electric field inside the cavity will be zero, even though the shell may not be spherical.
and on the outer surface of shell is
(b) The electric flux linked with any closed surface S inside the conductor is zero as electric field inside conductor is zero.
So, by Gauss’s theorem net charge enclosed by closed surface S is also zero i.e.,
So, if there is no charge inside the cavity, then there cannot be any charge on the inner surface of the shell and hence electric field inside the cavity will be zero, even though the shell may not be spherical.
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