CBSE Class 12 · 2009 · ElectrostaticsShort Answer

(a) A charge

+ Q

is placed on a large spherical conducting shell of radius

R

. Another small conducting sphere of radius

r

carrying charge

q

is introduced inside the large shell and is placed at its centre. Find the potential difference between two points, one lying on the sphere and the other on the shell.
(b) How would the charge between the two flow if they are connected by a conducting wire? Name the device which works on this fact.

Solution

(a) Potential at the surface of the inner sphere (radius

r

V (r) = \frac{1}{4 π ε _{0}} (\frac{q}{r} + \frac{Q}{R})

. Potential at the shell (radius

R

V (R) = \frac{1}{4 π ε _{0}} (\frac{q}{R} + \frac{Q}{R})

. So

V (r) - V (R) = \frac{q}{4 π ε _{0}} (\frac{1}{r} - \frac{1}{R})

, which is independent of

Q

. (b) Since

r < R

, this difference is positive for positive

q

, so on connecting them the charge

q

flows from the inner sphere to the outer shell (regardless of the shell's own charge

Q

). The Van de Graaff generator is based on this fact.

CBSE Class 12 Board · 2009 · Subjective

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CBSE Class 12 · 2009 · ElectrostaticsShort Answer

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