Question

A coil of resistance 200 $\Omega$ is placed in a magnetic field. If the magnetic flux $\phi$ (in weber) linked with the coil varies with time 't' (in second) as per the equation $\phi = 50t^2 + 4$, then the current induced in the coil at a time t = 2 s is

• A. 2 A
• B. 1 A
• C. 0.5 A
• D. 0.1 A

Hint:

Induced emf = -d$\phi$/dt. Current = |emf|/Resistance.

Answer 1

The Correct Option is B

Faraday's law states that the induced electromotive force (emf) in a coil is equal to the negative rate of change of magnetic flux linked with it. Mathematically, $$ \text{emf} = -\frac{d\phi}{dt} $$ Given $\phi = 50t^2 + 4$, we have $$ \text{emf} = -\frac{d}{dt}(50t^2 + 4) = -100t $$ At $t = 2 \, \text{s}$, $\text{emf} = -100(2) = -200 \, \text{V}$. The negative sign indicates the direction of the induced emf, but we are interested in the magnitude of the current. Ohm's law states that $V = IR$, where $V$ is the voltage, $I$ is the current, and $R$ is the resistance. Here, the induced emf acts as the voltage. Thus, $$ I = \frac{|\text{emf}|}{R} = \frac{200}{200} = 1 \, \text{A} $$