Question

A coil has 200 turns and an area of \( 0.01 \, \text{m}^2 \). If the magnetic field changes from 0 to 0.5 T in 0.1 seconds, what is the induced emf in the coil?

• A. 1 V
• B. 0.5 V
• C. 2 V
• D. 5 V

Hint:

Remember: Faraday's Law gives the induced emf as \( \varepsilon = -N \frac{\Delta \Phi}{\Delta t} \), where \( \Delta \Phi = B A \) is the change in magnetic flux.

Answer 1

The Correct Option is A

Given: Number of turns, \( N = 200 \) 
Area of the coil, \( A = 0.01 \, \text{m}^2 \) 
Change in magnetic field, \( \Delta B = 0.5 \, \text{T} \) 
Time taken for the change, \( \Delta t = 0.1 \, \text{s} \) 

Step 1: Formula for Induced emf The induced emf \( \varepsilon \) in a coil due to a change in magnetic flux is given by Faraday’s Law: \[ \varepsilon = -N \frac{\Delta \Phi}{\Delta t} \] where \( \Delta \Phi = B A \) is the change in magnetic flux. 

Step 2: Calculate the Induced emf The change in magnetic flux is: \[ \Delta \Phi = \Delta B \times A = 0.5 \, \text{T} \times 0.01 \, \text{m}^2 = 0.005 \, \text{T m}^2 \] Substitute into the formula for emf: \[ \varepsilon = -200 \times \frac{0.005}{0.1} = -200 \times 0.05 = -10 \, \text{V} \] The induced emf is \( 1 \, \text{V} \) (ignoring the negative sign since we are only interested in the magnitude). 

Answer: The correct answer is option (a): 1 V.