Question

A coil having 100 square loops each of side 10 cm is placed such that its plane is normal to a magnetic field, which is changing at a rate of \( 0.7 \ \text{T s}^{-1} \). The emf induced in the coil is

• A. \( 0.2 \ \text{V} \)
• B. \( 0.4 \ \text{V} \)
• C. \( 0.7 \ \text{V} \)
• D. \( 1 \ \text{V} \)

Hint:

Always convert dimensions into SI units before applying formulas in electromagnetism, especially for area and magnetic field.

Answer 1

The Correct Option is C

Step 1: Use Faraday’s Law of electromagnetic induction
\[ \text{emf} = N . A . \frac{dB}{dt} \] Step 2: Given data
Number of loops, \( N = 100 \)
Side of each square loop = \( 10 \ \text{cm} = 0.1 \ \text{m} \Rightarrow A = (0.1)^2 = 0.01 \ \text{m}^2 \)
Change in magnetic field, \( \frac{dB}{dt} = 0.7 \ \text{T/s} \) Step 3: Substituting values
\[ \text{emf} = 100 . 0.01 . 0.7 = 0.7 \ \text{V} \]