Question

A coil of area 10 ${cm}^2$ and 10 turns is in magnetic field directed perpendicular to the plane and changing at a rate of ${10}^8$ gauss /s The resistance of coil is 20 $\Omega$ . The current in the coil will be

• A. 0.5 A
• B. $5\times {10}^{-3}A$
• C. 0.05 A
• D. 5 A

Answer 1

The correct option is C 0.05 A

$\text{Given}$ : Cross sectional area A = 10cm² =10${}^{-3}$ m²
number of turns, N = 10

change of magnetic field per unit time , $\frac{dB}{dt}$ = 10${}^8$ Gauss /s = 10${}^4$ T/s
resistance of coil , R = 20 ohms

$\text{To find}$ : Current

$\text{Solution}$ :

Now, induced emf = -$\frac{d\varphi }{dt}$

= - N$\times A\times \frac{dB}{dt}$
= - (10 × 10${}^{-3}$ × 10${}^4$ )

= - 1V
Hence, induced emf = 1V
We know that the induced current = $\frac{inducedemf}{R}$

= $\frac{1}{20}$= 0.05 Ampere
$\text{Hence option C is correct}$