Question

A coil has 100 turns, each of area \( 0.05 \, \text{m}^2 \) and total resistance \( 1.5 \, \Omega \). It is inserted at an instant in a magnetic field of \( 90 \, \text{mT} \), with its axis parallel to the field. The charge induced in the coil at that instant is:

• A. \( 3.0 \, \text{mC} \)
• B. \( 0.30 \, \text{C} \)
• C. \( 0.45 \, \text{C} \)
• D. \( 1.5 \, \text{C} \)

Hint:

Remember that the induced charge is related to the change in magnetic flux through the coil, and depends on the number of turns, the area, and the magnetic field strength.

Answer 1

The Correct Option is B

Faraday's law describes the induced charge \( Q \) in a coil as: \[ Q = \frac{N \cdot A \cdot B}{R} \cdot \Delta t \] with the following parameters: \( N = 100 \) turns, \( A = 0.05 \, \text{m}^2 \) per turn, \( B = 0.09 \, \text{T} \) (given as \( 90 \, \text{mT} \)) magnetic field strength, and \( R = 1.5 \, \Omega \) total coil resistance.

Substituting these values yields: \[ Q = \frac{100 \cdot 0.05 \cdot 0.09}{1.5} = 0.30 \, \text{C} \] The computed induced charge is \( 0.30 \, \text{C} \).