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Physics · Electromagnetic induction: Faraday's law, induced emf and current, Lenz's law, eddy currents, self and mutual inductance

A circuit consists of a coil with inductance and an uncharged capacitor of capac

A circuit consists of a coil with inductance \( L \) and an uncharged capacitor of capacitance C.The coil is in a constant uniform magnetic field such that the flux through the coil is \( \mathbf{\Phi} . \mathbf{A t} \) time \( t=0, \) the magnetic field is abruptly switched off. Let \( \omega_{0}=1 / \sqrt{L C} \) and ignore the resistance of the circuit. Then:

  • A. current in the circuit is \( I(t)=(\Phi / L) \cos \omega_{0} t \)
  • B. Magnitude of the charge on the capacitor is \( |Q(t)|= \) \( 2 C \omega_{0} \mid \sin \omega_{0} t \)
  • C. initial current in the circuit is infinite
  • D. initial charge on the capacitor is \( C \omega_{0} \Phi \)

Step-by-step solution

Initially, the flux through the coil is Φ. When the field is switched off, the induced emf sets the initial current I(0)=Φ/L (from flux conservation). The circuit then oscillates as an LC circuit with ω0=1/√(LC). Solving the differential equation yields I(t)= (Φ/L) cos(ω0 t).
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