Methods of producing induced emf Class 12

There are various methods of producing induced emf in any electrical circuit. From Faraday’s law of electromagnetic induction, we know that an EMF can be induced in any electrical circuit by changing magnetic flux w.r.t time. In this article, we will talk about the methods by which we can produce induced EMF in any coil or circuit. So let’s get started…

Methods of producing induced emf

An induced emf can be produced by changing the magnetic flux linked with the circuit. The magnetic flux is given by $$\phi=BA\cos\theta$$ This flux can be changed by altering any of the components associated with magnetic flux.

• Changing magnetic field, B
• Changing the area A of the coil, and
• Changing the relative orientation $\theta$ of B and A.

Induced EMF by changing the magnetic field B

Magnetic flux is directly proportional to the magnetic field B, i.e if the change in the magnetic field is increased then the change in magnetic flux also increases, and if the change in the magnetic field is decreased then the change in magnetic flux also decreases.

Read Also

• Faraday and henry’s experiments on electromagnetic induction
• Faraday’s laws of electromagnetic induction Class 12

In the above-linked article ☝️, we have discussed that an emf is induced in the coil by changing the magnetic flux through it by

• moving a magnet towards a stationary coil.
• moving a coil towards a stationary magnet.
• varying currents in the nearby coil.

Induced emf by changing the area of the coil

Let the conductor PQ moved inwards with its speed $v$. As the conductor, slides towards the left, the area of the rectangular loop PQRS decreases. This decreases the magnetic flux linked with the closed loop.

Suppose, a length $x$ of the loop lies inside the magnetic field at any instant of time $t$. Then the magnetic flux linked with rectangular loop PQRS is $$\phi=B\cdot A=Blx$$

According to the Faraday’s law of electromagnetic induction, induced EMF is given as $${\mathcal {E}}=-\frac{d\phi}{dt}=-\frac{d}{dt}(Blx)=-Bl\frac{dx}{dt}$$ or $$|{\mathcal {E}}|=Blv$$ According to the fleming’s right hand rule, induced currents flows in the anti-clockwise direction.

Read Also

• Motional EMF from Faraday’s law | definition, formula derivation

Induced emf by changing relative orientation of the coil in the magnetic field

Consider a coil PQRS free to rotate in a uniform magnetic field $\overrightarrow{B}$. The axis of rotation of the coil is perpendicular to the field $\overrightarrow{B}$. The flux through the coil, when normal makes an angle $\theta$ with the field, is given by $$\phi=BA\cos\theta$$Where $A$ is the area of the coil.

If the coil rotates with an angular velocity $\omega$ and turns through an angle $\theta$ in time $t$, then $$\theta=\omega t, \quad \therefore\quad \phi=BA\cos\omega t$$

As the coil rotates, the magnetic flux linked with it changes. An induced emf is set up in the coil which is given by $$\varepsilon=-\frac{d\phi}{dt}=-\frac{d}{dt}(BA\cos\omega t)=BA\omega\sin\omega t$$ If the coil have $N$ turns, then the total induced emf will be $$\mathcal{E}=NBA\omega\sin\omega t$$ Thus, the induced emf varies sinusoidally with time $t$. The value of induced emf is maximum when $\sin\omega t=1$ or $\omega t=90^{\circ}$, i.e when the plane of the coil is parallel to the field $\overrightarrow{B}$. Denoting this maximum value of emf by $\mathcal{E_0}$, we have $$\mathcal{E_0} =NBA\omega=2\pi f NBA$$ $$\therefore\quad \mathcal{E}=\mathcal{E_0}\sin\omega t=\mathcal{E_0}\sin2\pi ft$$ Where $f$ is the frequency of the rotation of the coil.

Some special cases

1. When $\omega t= 0^{\circ}$, and the plane of the coil is perpendicular to the $\overrightarrow{B}$. $$\sin\omega t=\sin{0^{\circ}}=0, \; \text{so that}\; \mathcal{E}=0$$ 2. When $\omega t= \frac{\pi}{2}$, the plane of the coil is parallel to the $\overrightarrow{B}$. $$\sin\omega t=\sin\frac{\pi}{2}=1, \; \text{so that}\; \mathcal{E}=\mathcal{E_0}$$ 3. When $\omega t= \pi$, the plane of the coil is again perpendicular to the $\overrightarrow{B}$. $$\sin\omega t=\sin\pi=0, \; \text{so that}\; \mathcal{E}=0$$ 4. When $\omega t= \frac{3\pi}{2}$, the plane of the coil is again parallel to the $\overrightarrow{B}$. $$\sin\omega t=\sin\frac{3\pi}{2}=-1, \; \text{so that}\; \mathcal{E}=-\mathcal{E_0}$$ 5. When $\omega t= 2\pi$, the plane of the coil is again perpendicular to the $\overrightarrow{B}$ after completing one revolution. $$\sin\omega t=\sin2\pi=0, \; \text{so that}\; \mathcal{E}=0$$

As the coil continues to rotate in the same sense, the same cycle of changes repeats again and again. As shown in the above figure, the graph between emf $\mathcal{E}$ and time $t$ is a sine curve. Such an emf is called sinusoidal or alternating emf. Both the magnitude and the direction of this emf change continuously with time.

The fact that an induced emf is set up in the coil or wire rotated in a magnetic field forms the basic principle of generator and dynamo.

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