Faradays Laws Of Induction

To determine the self-inductance of the coil, we can use the following formula that relates the induced electromotive force (emf) in a coil to its self-inductance and the rate of change of current through it:

Where:

• is the induced emf (0.1 V in this case).
• is the self-inductance of the coil.
• is the change in current (-2 A to +2 A, so ).
• is the time interval over which the current changes (0.2 s).

Rearranging the formula to solve for , we have:

Substitute the given values into this formula:

Since inductance is conventionally given as a positive value, we take the absolute value:

Thus, the self-inductance of the coil is 5 mH.

Let's analyze the options:

• 5 mH: Correct, matches calculated value.
• 1 mH: Incorrect.
• 2.5 mH: Incorrect.
• 4 mH: Incorrect.

Therefore, the correct answer is 5 mH.

To find the induced current in the circuit at , we first need to determine the electromotive force (emf) induced in the circuit using Faraday's Law of electromagnetic induction. The emf ( ) is given by the negative rate of change of magnetic flux ( ) with respect to time, . Given , we differentiate: .

Substitute into the derivative:

The induced emf is

Using Ohm's Law, , with resistance :

The computed current, , fits the expected range of 2 to 2 A. Therefore, the induced current at is