Question

Figure shows two coaxial coils $M$ and $N$. Column I is regarding some operations done with coil $M$ and Column II about induced current in coil $N$.

$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \text{i}& \text{Just after switch S is closed}& \text{a}& \text{Current is induced A to B}\\ \text{ii}& \text{Switch S is opened after}& \text{b}& \text{Current is induced from B to}\\ & \text{keeping it closed for a long}& & \text{A}\\ \text{iii}& \text{After switch S is closed for a}& \text{c}& \text{Nocurrent is induced}\\ & \text{long time}& & \end{array}$

• A. i - a; ii - b; iii - c
• B. i - a; ii - c; iii - b
• C. i - c; ii - b; iii -a
• D. i - b; ii - a; iii -c

Answer 1

The correct option is A i - a; ii - b; iii - c

Case (i): When the switch is just closed.
Current starts flowing in the coil M and a magnetic field(B) is developed whose direction (right to left) can be found by loop rule. Due to this, flux through N changes and current is induced such that it opposes the magnetic field due to coil M. Hence direction of current in the coil N will be opposite (i.e A to B) to that in coil M as shown in figure.

Case (ii): When the switch is opened after keeping it closed for a long time, steady state will be reached i.e current might have reached its maximum value. When the switch is open, currents starts decreasing in the coil M leading to decrease in magnetic field(B). To oppose this decrement in magnetic field, flux changes through coil N such that it supports magnetic field. For magnetic field(B') to support magnetic field in coil M, current induced in coil N (from loop rule) should be in same direction(i.e B to A) as it is in coil M as shown figure below.
Case (iii): When the switch is closed from a long time, current in the coil M will reach the maximum value and becomes constant. If current remains constant magnetic field developed will also remain constant. Since magnetic field remains constant in coil M, change in flux in coil N will be zero and therefore there won't be any emf induced in coil N. Since there is no emf induced, no current will be induced in coil N.