Question

A rectangular wire loop of resistance \(1.5\Omega\) placed in a region of uniform magnetic field of magnitude \(0.3\) T directed normal to the loop. If the area of the loop decreases at a rate of \(0.05\) \(\text{m}^{2}/s\) in this magnetic field, the heat produced in it is \(x\times 10^{-6}\) W. The value of \(x\) is

• A. \(1.5\)
• B. \(15\)
• C. \(2\)
• D. \(150\)

Hint:

Find the induced emf from the rate of change of area, then the power from emf squared over resistance.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
Induced emf is \(\varepsilon=\dfrac{d\Phi}{dt}=B\dfrac{dA}{dt}\), and heating power is \(P=\dfrac{\varepsilon^2}{R}\).

Step 2: Emf
\(\varepsilon=0.3\times0.05=0.015\) V.

Step 3: Power
\(P=\dfrac{(0.015)^2}{1.5}=\dfrac{2.25\times10^{-4}}{1.5}=1.5\times10^{-4}\) W.

Step 4: Result
\(P=150\times10^{-6}\) W, so \(x=150\), option (D).

Final Answer:
The value of x is 150. \[ \boxed{\text{(D) }150} \]