Question

A coil of 45 turns and radius 4 cm is placed in a uniform magnetic field such that its plane is perpendicular to the direction of the field. If the magnetic field increases from 0 to 0.70 T at a constant rate in a time interval of 220 s, then the induced emf in the coil is

• A. 0.32 mV
• B. 0.50 mV
• C. 0.72 mV
• D. 0.96 mV

Hint:

Use Faraday’s law: \( \mathcal{E} = N \cdot \frac{d\Phi}{dt} \). Remember to convert radius into meters and compute the area using \( A = \pi r^2 \).

Answer 1

The Correct Option is C

Step 1: Use Faraday's law of electromagnetic induction.
Induced emf: \[ \mathcal{E} = N \cdot \frac{d\Phi_B}{dt} = N \cdot \frac{d(B \cdot A)}{dt} \] Step 2: Insert given values.
\[ N = 45, \, r = 4\, \text{cm} = 0.04\, \text{m}, \, A = \pi r^2 = \pi (0.04)^2 = 5.0265 \times 10^{-3} \, \text{m}^2 \] \[ \frac{dB}{dt} = \frac{0.70 - 0}{220} = 3.18 \times 10^{-3} \, \text{T/s} \] Step 3: Calculate emf. \[ \mathcal{E} = 45 \cdot 5.0265 \times 10^{-3} \cdot 3.18 \times 10^{-3} \approx 0.000717 \, \text{V} = 0.717 \, \text{mV} \approx 0.72 \, \text{mV} \] Step 4: Select the correct option.
The induced emf is approximately 0.72 mV, which matches option (3).