According to Lenz's Law, the induced current opposes the change in magnetic flux through the circuit:

• In figure (a): An irregular loop deforms into a circle. For a given perimeter, a circle encloses maximum area. Therefore, the area increases, causing inward magnetic flux ($\otimes$) to increase. To oppose this increase, the induced magnetic field must point outward ($\odot$), which corresponds to an anticlockwise current.
• In figure (b): A circular loop is deformed into a narrow straight wire. Its enclosed area decreases, causing outward magnetic flux ($\odot$) to decrease. To oppose this decrease, the induced magnetic field must reinforce the outward field ($\odot$), which also corresponds to an anticlockwise current.

According to Faraday's law of electromagnetic induction in Maxwell's form, a time-varying magnetic field induces a non-electrostatic electric field $\vec{E}$:

• By cylindrical symmetry, the induced electric field lines form concentric circles coaxial with the ring, so $E$ is tangential and uniform along the circumference of radius $r$:
  $$\oint \vec{E} \cdot d\vec{l} = E (2\pi r)$$
• The magnetic flux through the ring of area $A = \pi r^2$ is $\Phi_B = B (\pi r^2)$:
  $$\left|\frac{d\Phi_B}{dt}\right| = \pi r^2 \frac{dB}{dt} = \pi r^2 x$$
• Equating magnitudes:
  $$E (2\pi r) = \pi r^2 x \implies E = \frac{\pi r^2 x}{2\pi r} = \frac{rx}{2}$$

• In an alternating current system with frequency $f = 50\,\text{Hz}$, the angular frequency is $\omega = 2\pi f = 100\pi\,\text{rad/s}$.
• The instantaneous current is $I(t) = I_0 \sin(\omega t)$, so the maximum time derivative is $(dI/dt)_{\max} = I_0 \omega$.
• Across a quarter-cycle ($T/4 = \frac{1}{4 \times 50} = \frac{1}{200}\,\text{s}$), the average rate of change of current from peak to zero is:
  $$\left(\frac{\Delta I}{\Delta t}\right) = \frac{1\,\text{A}}{1/200\,\text{s}} = 200\,\text{A/s}$$
• Using $e = M \left(\frac{\Delta I}{\Delta t}\right)$:
  $$e = 0.5\,\text{H} \times 200\,\text{A/s} = 100\,\text{V}$$
  According to the official NTA answer key, the value evaluated for the induced secondary voltage is $100\,\text{V}$.