ElectroMagnetic InductionVery Hard
Question
A coil of wire having finite inductance and resistance has conducting ring placed co-axially with in it. The coil is connected to a battery at time t = 0, so that a time dependent current I1(t) start flowing through the coil. If I2(t) is the current induced in the ring and B(t) is the magnetic field at the axis of the coil due to I1(t) then as a function of time (t > 0), the product I2(t)B(t)
Options
A.increases with time
B.decreases with time
C.does not very with time
D.passes through a maximum
Solution
The equation of I1(t), I2(t) and B(t) will take following forms :
I1(t) = K1(1 - e-k2t) → current growth in L-R circuit
B(t) = K3(1 - e-k2t) → B(t) ∝ I1(t)
I2(t) = K4e-k2t)
Therefore, the product I2(t) B(t) = K5e-k2t(1 - e-k2t).
The value of this product is zero at t = 0 and t = ∞ Therefore, the product will pass through a maximum value. The corresponding graphs will be as follows :
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