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

The induced charge in the coil is given by Faraday's law: \[ Q = \frac{N \cdot A \cdot B}{R} \cdot \Delta t \] where:
\( N = 100 \) is the number of turns,
\( A = 0.05 \, \text{m}^2 \) is the area of each turn,
\( B = 90 \, \text{mT} = 0.09 \, \text{T} \) is the magnetic field strength,
\( R = 1.5 \, \Omega \) is the total resistance of the coil.

Substitute these values into the formula: \[ Q = \frac{100 \cdot 0.05 \cdot 0.09}{1.5} = 0.30 \, \text{C} \] Thus, the correct answer is \( 0.30 \, \text{C} \).