Question

A coil (100 turns, radius 3 cm, resistance 4 \(\Omega\)) is co-axial with solenoid (200 turns/cm, diameter 4 cm). Solenoid current drops from 2 A to 0 in 0.04 s. Find induced current.

• A. \( 4\pi^2\ \text{mA} \)
• B. \( 8\ \text{mA} \)
• C. \( 30.3\ \text{mA} \)
• D. \( 45.5\ \text{mA} \)

Hint:

Use \( \Phi = NBA \), and \( \text{emf} = -\frac{d\Phi}{dt} \), \( I = \frac{e}{R} \).

Answer 1

The Correct Option is A

Magnetic field in solenoid: \[ B = \mu_0 n I,\quad n = 20000\ \text{turns/m} \] Change in flux: \[ \Delta \Phi = NAB = N (\pi r^2) \cdot (\mu_0 n \Delta I) = 100 \cdot \pi (0.03)^2 \cdot 4\pi \times 10^{-7} \cdot 20000 \cdot 2 \] \[ = 100 \cdot \pi \cdot 9 \times 10^{-4} \cdot 4\pi \times 10^{-7} \cdot 4 \times 10^4 \Rightarrow e = \frac{\Delta \Phi}{\Delta t},\quad I = \frac{e}{R} = 4\pi^2\ \text{mA} \]