Electromagnetic Induction - Result Question 7

7. A coil of resistance $400 \Omega$ is placed in a magnetic field. If the magnetic flux $\phi$ (wb) linked with the coil varies with time $t$ (sec) as $\phi=50 t^{2}+4$. The current in the coil at $t=2 sec$ is :

[2012]

(a) $0.5 A$

(b) $0.1 A$

(c) $2 A$

(d) $1 A$

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Answer:

Correct Answer: 7. (a)

Solution:

  1. (a) According, to Faraday’s law of induction

Induced e.m.f. $\varepsilon=-\frac{d \phi}{d t}=-(100 t)$

Induced current $i$ at $t=2 sec$.

$=|\frac{\varepsilon}{R}|=+\frac{100 \times 2}{400}=+0.5 A$

The magnetic flux linked with a loop does not change when magnet and loop are moving with the same velocity.