Question

A circular coil of area 200cm, 500 turns and 2 ohm resistance is palced. With its plane perpendicular to the horizontal component of earth magnetic field. It is rotated about its vertical diameter through 180degree in 0.25 sec. If the magnetic induction of earth magnetic field is 500.And the angle of dip is 37degree at the palce then induced current in the coil is

Answer 1

Answer: The induced current in the coil is 31400 A.

Explanation:

Given that,

Area of coil $A = 200 cm^{2}$

Number of turns N = 500

Resistance r = 2 ohm

Time $t = 0.25 s$

Angle $\theta  = 180^{0}$

Magnetic field $B = 500 T$

We know that,

The magnetic flux through the circular coil at any instantdBAcos($\phi = NBAcos\theta$

We know,

$\dfrac{\theta}{t} = \omega$

$\dfrac{180^{0}}{0.25s}$

$\omega = 720 = 4\pi$

We know that,

The induced Emf is

$E = -\dfrac{d\phi}{dt}$

$E = - dBNAcos(\omega t) dt$

$E = NBA\omega sin(\omega t)$

$E = 500\times500\times2\ m^{2}\times4\pi$

$E = 62800 V$

Now, the induced current is

$I = \dfrac{E}{r}$

$I = \dfrac{62800\ V}{2\ \Omega}A$

$I = 31400 A$

Hence, the induced current in the coil is 31400 A.