A coil of wire having finite inductance and resistance has a conducting ring placed coaxially within it. The coil is connected to a battery at time t=0, so that a time dependent
current I₁(t) starts flowing through the coil. If l₂(t) is the current induced in the ring and B(t) is the magnetic field at the axis of the coil due to l₁(t), then as a function of time (t > 0), the product I₂(t) B(t)

Question

Infinity Learn · Accepted Answer

Using $$k1$$,$$k2$$ etc, as different constants. $$I1(t)=k11$$−e−$$t/$$τ,$$B(t)=k2I1(t)I2(t)=k3dB(t)dt=k4e$$−$$t/$$τ∴$$I2(t)B(t)=k51$$−e−$$t/$$τe−$$t/$$τThis quantity is zero for t $$=$$ $$0$$ and t $$=$$ ∞ and positive for other value of t. It must, therefore, pass through a maximum.

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