Question

Q 22 - Single
A loop of area 0.1 m2 rotates with a speed
of 60 rps perpendicular to a magnetic field
of 0.4 T. If there are 100 turns in the loop,
maximum voltage induced in the loop is
A
15.07 V
B
1507 V
с
250 V
D
150 V​

Answer 1

Given:

A loop of area 0.1 m2 rotates with a speed

of 60 rps perpendicular to a magnetic field

of 0.4 T ; there are 100 turns in the loop.

To find:

Max voltage induced in the loop.

Calculation:

Induced voltage is given as :

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

$= > \: E = - \dfrac{d \{NBA \cos( \theta) \} }{dt}$

$= > \: E = - NBA \times \dfrac{d \{ \cos( \theta) \} }{dt}$

$= > \: E = NBA \sin( \theta) \times \dfrac{d \theta }{dt}$

$= > \: E = NBA \sin( \theta) \times \omega$

For max induced EMF:

$= > \: E_{max}= NBA \times \omega$

$= > \: E_{max}= 100 \times 0.4 \times 0.1 \times (60 \times 2\pi)$

$= > \: E_{max}= 4 \times (60 \times 2\pi)$

$= > \: E_{max}= 4 \times 120\pi$

$= > \: E_{max}= 480\pi$

$\boxed{ \bold{= > \: E_{max} \approx 1507 \: volts}}$

HOPE IT HELPS.