Question

A boy peddles a stationary bicycle. The pedals of the bicycle are attached to a 200 turn coil of area 0.10 m². The coil rotates at half a revolution per second and it is placed in a uniform magnetic field of 0.02T perpendicular to the axis of rotation of the coil. The maximum voltage generated in the Coil is then
A 1.26 V
B 2.16 V
C 3.24 V
D 4.12 V

Answer 1

Here we will approach the question by using the concept of magnetic field and electromagnetic induction.
Use $\omega = 2\pi v$ where $v$ = frequency.
Electromagnetic or magnetic induction is the production of an electromotive force across an electrical conductor in a changing magnetic field.

Formula: Rate of change of flux = $e.m.f. = NBA\omega$

Complete step by step solution:
Given,
$v = 0.5Hz$, $N = 200$, $A = 0.1{m^2}$ and $B = 0.02T$
$v$ = frequency
N = no. of turns
A = Area
B = magnetic field

Using formula, $e.m.f. = NBA\omega$ since perpendicular to the axis of rotation of the coil i.e. $\sin {90^ \circ } = 1$
Maximum voltage generated = $NBA\omega = NBA\left( {2\pi v} \right) = 200 \times 0.02 \times \left( {2\pi \times 0.5} \right) = 1.26V$

Thus the correct answer is option A. 1.26 V

Note: When a conductor is moved through a magnetic field, an EMF is generated and the interaction of the magnetic field produced by the conductor with the magnetic field that was present causes deflection.