A solid conducting sphere of radius 10 cm is enclosed by a thin metallic shell of radius 20 cm. A charge q=20 μ C is given to the inner sphere. Find the heat generated in the process when the inner sphere is connected to the shell by a conducting wire.

Question

A solid conducting sphere of radius 10 cm is enclosed by a thin metallic shell of radius 20 cm. A charge q=20 μ C is given to the inner sphere. Find the heat generated in the process when the inner sphere is connected to the shell by a conducting wire. (A) 12 J (B) 9 J (C) 24 J (D) zero

Tardigrade Admin · Accepted Answer

On connecting, the entire amount of charge will shift to the outer sphere. Heat generated is Ui-Uf =(q2/8 π ε0 R1)-(q2/8 π ε0 R2) =((20 × 10-6) × 9 × 109/2)[(1/0.10)-(1/0.20)]=9 J

Q. A solid conducting sphere of radius $10 c m$ is enclosed by a thin metallic shell of radius $20 c m$ . A charge $q = 20 μ C$ is given to the inner sphere. Find the heat generated in the process when the inner sphere is connected to the shell by a conducting wire.

$12 J$

$9 J$

$24 J$

zero

On connecting, the entire amount of charge will shift to the outer sphere. Heat generated is
$U_{i} - U_{f} = \frac{q ^{2}}{8 π ε _{0} R _{1}} - \frac{q ^{2}}{8 π ε _{0} R _{2}}$
$= \frac{( 20 \times 1 0 ^{- 6} ) \times 9 \times 1 0 ^{9}}{2} [\frac{1}{0.10} - \frac{1}{0.20}] = 9 J$

Q. A solid conducting sphere of radius 10cm is enclosed by a thin metallic shell of radius 20cm. A charge q=20μC is given to the inner sphere. Find the heat generated in the process when the inner sphere is connected to the shell by a conducting wire.

12J

9J

24J