Question

Prakash peddles a stationary bicycle, the pedals of which are attached to a $100$ turn coil of area $0.1\,{m^2}$. The coil rotates at half a revolution per second and it is placed in a uniform magnetic field of $0.01\,T$ perpendicular to the axis of rotation of the coil. Determine the maximum voltage generated in the coil.

Answer 1

Hint: Using Faraday’s law of induction which states that change in magnetic flux induces electromotive force. This induced emf is the required maximum voltage. Using the formula of induced emf we will solve the given question.

Formula used:
$E = NAB\omega $
Where $E$ is the induced electromotive force, $N$ is the number of turns in the coil, $A$ is the area of cross section, $B$ is the magnetic field, $\omega $ is the angular frequency.

Complete step by step answer:
Induction is caused by a changing magnetic flux, which then induces an electromotive force, emf, in a circuit. This important law of electromagnetism is also known as Faraday's law of induction.
Given the number of turns in the coil $N = 100$.
Area of cross section of the coil $A = 0.1{m^2}$.
Since the coil rotates at half a revolution per second, frequency will be $f = \dfrac{1}{2}Hz$.
Magnetic field $B = 0.01T$
Using the formula of emf induced,
$E = NAB\omega $
$\because \omega = 2\pi f$
$ \Rightarrow E = NAB2\pi f$
Putting the values from above, we get
$ \Rightarrow E = 100 \times 0.1 \times 0.01 \times 2 \times \dfrac{{22}}{7} \times \dfrac{1}{2}$
$ \therefore E = 0.31\,V$

Hence, the maximum voltage generated in the coil is $E = 0.31\,V$.

Note: There are two important laws of Faraday’s which are given below as:
Faraday’s First law: When a conductor is put in a fluctuating magnetic field, an induced emf is produced, and if the conductor is a closed circuit, an induced current flows through it.
Faraday’s second law: The magnitude of the induced EMF is equal to the rate of change in flux connections, according to the second law.