Question

The magnetic flux in a closed circuit of resistance \(10 \, \Omega\) varies with time as \( \phi = (2t - 4t^2 + 1) \). The current in the loop will change its direction after a time of

• A. 0.25 sec
• B. 0.5 sec
• C. 1 sec
• D. none

Hint:

The direction of the induced current in a circuit changes when the magnetic flux through the circuit changes sign.

Answer 1

The Correct Option is B

Step 1: Faraday's Law.
According to Faraday's law of induction, the induced emf is given by: \[ \epsilon = - \frac{d\phi}{dt} \] where \( \phi \) is the magnetic flux. Substituting the given flux equation \( \phi = (2t - 4t^2 + 1) \), we get: \[ \epsilon = - \frac{d}{dt}(2t - 4t^2 + 1) \] Step 2: Determining the Direction Change.
For the current to change direction, the sign of the induced emf must change. Solving for \( \epsilon \), we get the time at which this change occurs at \( t = 0.5 \, \text{sec} \). Step 3: Conclusion.
The correct answer is (B), 0.5 sec.