Question

When a current of \( 4 \, \text{mA} \) passes through an inductor, if the flux linked with it is \( 32 \times 10^{-6} \, \text{Tm}^2 \), then the energy stored in the inductor is:

• A. \( 64 \times 10^{-9} \, \text{J} \)
• B. \( 32 \times 10^{-9} \, \text{J} \)
• C. \( 128 \times 10^{-9} \, \text{J} \)
• D. \( 96 \times 10^{-9} \, \text{J} \)

Hint:

The energy stored in an inductor is proportional to the square of the current and the inductance. Use the relationship $ \Phi = L I $ to find the inductance when the flux and current are known.

Answer 1

The Correct Option is A

Step 1: Known Information.
Current through the inductor: \( I = 4 \, \text{mA} = 4 \times 10^{-3} \, \text{A} \)
Flux linked with the inductor: \( \Phi = 32 \times 10^{-6} \, \text{Tm}^2 \)
Energy stored in an inductor is given by: \[ U = \frac{1}{2} L I^2 \] where \( L \) is the inductance of the inductor.
Step 2: Relate Flux and Inductance.
The flux linked with the inductor is related to the inductance and current by: \[ \Phi = L I \] Solve for \( L \): \[ L = \frac{\Phi}{I} \] Substitute the given values: \[ L = \frac{32 \times 10^{-6}}{4 \times 10^{-3}} = 8 \times 10^{-3} \, \text{H} \] Step 3: Calculate the Energy Stored.
Using the formula for energy stored in an inductor: \[ U = \frac{1}{2} L I^2 \] Substitute \( L = 8 \times 10^{-3} \, \text{H} \) and \( I = 4 \times 10^{-3} \, \text{A} \): \[ U = \frac{1}{2} \cdot 8 \times 10^{-3} \cdot (4 \times 10^{-3})^2 \] Simplify: \[ U = \frac{1}{2} \cdot 8 \times 10^{-3} \cdot 16 \times 10^{-6} \] \[ U = 4 \times 10^{-3} \cdot 16 \times 10^{-6} \] \[ U = 64 \times 10^{-9} \, \text{J} \] Final Answer: \( \boxed{64 \times 10^{-9} \, \text{J}} \)