Electromagnetic Induction and Alternating Current 7 Question 12

12. A coil of wire having finite inductance and resistance has a conducting ring placed co-axially 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 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)

(2000,2M)

(a) increases with time

(b) decreases with time

(c) does not vary with time

(d) passes through a maximum

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Answer:

Correct Answer: 12. (d)

Solution:

  1. The equations of I1(t),I2(t) and B(t) will take the following forms :

I1(t)=K1(1ek2t) current growth in LR circuit B(t)=K3(1ek2t)B(t)I1(t)I2(t)=K4ek2tI2(t)=e2R and e2dI1dt:e2=MdI1dt

Therefore, the product I2(t)B(t)=K5ek2t(1ek2t). 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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