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 dependentcurrent 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)
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a
Increases with time
b
Decreases with time
c
Does not vary with time
d
Passes through a maximum
answer is D.
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Detailed Solution
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.