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2 metal balls of rad r are placed at very large distance from each other. they are connercted by a coil of inductance l and a switch s. one sphere is given charge +q and switch is closed. after what time charge on sphere is reduced to half of its initial value?
As the whole system is placed at ground the circuit becomes closed loop and hence from KVL,V – Ldi/dt – V’ = 0V = Ldi/dt + V’kq/r = Ldi/dt + 0 (initially)kq/r = L*d^2q/dt^2Ld^2q = (kq/rL)dt^2qLdq = (kqt/rL)dt q^2*L = k*q*t^2/r*Lt^2 = qrL^2/kt = root(qrL/k)put q = q/2t = root(qrL/2k) s
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