Question

A 61.6 turns circular coil with radius 4.44 cm and resistance 2.34 Ω is placed in a magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies in time according to the expression B = a1 t + a2 t 2 , where a1 = 0.0411 Tsh, a2 = 0.044 M/s 2 are constants, time t is in seconds and field B is in Tesla. Find the magnitude of the induced emf in the coil at t = 9.21 s

Answer 1

Answer:

Induced emf is 0.324 V

Explanation:

We have,

Number of turns, n = 61.6

Radius of circular coil, r = 4.44 cm

Resistance of coil, R = 2.34 Ω

The magnitude of the magnetic field varies in time according to the expression :

$B=a_1t+a_2t^2$

$a_1=0.0411\\\\a_2=0.044$

The magnitude of the induced emf in the coil is given by :

$\epsilon=\dfrac{d\phi}{dt}\\\\\epsilon=\dfrac{d(NBA)}{dt}\\\\\epsilon=NA\dfrac{dB}{dt}$

$\epsilon=\pi r^2\dfrac{dB}{dt}$

At t = 9.21 s,

$\dfrac{dB}{dt}=(0.0411+2\times 0.044 \times 9.21)\\\\\dfrac{dB}{dt}=0.851\ T/s$

$\epsilon=61.6\times \pi \times (4.44 \times 10^{-2})^2\times 0.851$

$\epsilon=5.27\times 10^{-3}\ V$

So, the magnitude of the induced emf in the coil is 0.324 V