A solid conducting sphere of radius 'a' having charge q is surrounded by a concentric conducting spherical shell of inner radius 2a and outer radius 3a as shown in figure. The amount of heat

Question

A solid conducting sphere of radius 'a' having charge q is surrounded by a concentric conducting spherical shell of inner radius 2a and outer radius 3a as shown in figure. The amount of heat produced when switch is closed is α ( 24 a Kq 2 ​ ) . Fill the value of α .

TestHub · Accepted Answer

Before the switch closes, the field exists from $a$ to $2 a$ and beyond $3 a$ : $U_{i} = \frac{k q ^{2}}{2} (\frac{1}{a} - \frac{1}{2 a}) + \frac{k q ^{2}}{2} \cdot \frac{1}{3 a} = \frac{5 k q ^{2}}{12 a}$ .

After closing, all charge moves to the outer surface: $U_{f} = \frac{k q ^{2}}{6 a}$ .

Heat $= U_{i} - U_{f} = \frac{k q ^{2}}{4 a} = α (\frac{k q ^{2}}{24 a})$ → $α = 6$ .

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