Production of Induced emf in a Coil

# Objective

To demonstrate the production of induced emf in a coil due to the movement of

(i) a magnet towards and away from it.

(ii) similar coil carrying current towards and away from it.

# Theory

Michael Faraday discovered that a changing magnetic field induces an electromotive force (emf), a phenomenon known as electromagnetic induction.

Law of electromagnetic induction- The magnitude of the induced emf in a circuit is equal to the time rate of change of magnetic flux through the circuit.

Induced emf(ε)  =  - dΦB/dt

For a closely wound coil consisting of N turns, where the change in flux is consistent across each turn, the total induced electromotive force (emf) is expressed as follows.

Induced emf (ε)= - N( dΦB/dt)

ΦB = B.A = BA cos(θ)

Φ= magnetic flux

B = magnetic field

A = area through which the magnetic field lines pass

θ = angle between the magnetic field and surface

Magnetic flux can change by varying the magnetic field, the area through which the magnetic field lines pass, and the angle between the magnetic field and the surface.

The negative sign indicates that the induced emf (ε) opposes the change in magnetic flux.

Michael Faraday conducted different experiments to reach the law of electromagnetic induction. Let's familiarize these experiments to know which factors influence induced emf.

Experiment I

• Connect a coil with a galvanometer.  Move the magnet towards the coil (Fig 1). The pointer in the galvanometer deflects. It indicates the presence of the current. The pointer in the galvanometer deflects in the opposite direction when the magnet moves away from the coil. Deflection of the pointer in the galvanometer happens when the magnet moves towards the coil and away from the coil.

Fig 1: When the bar magnet is pushed towards the coil, the pointer in the galvanometer G deflects

• You can see the deflection of the pointer in the galvanometer in the opposite direction if you move the opposite face of the magnet towards the coil. The direction of deflection of the pointer in the galvanometer will be different when we bring the north pole of the magnet towards the coil and when we bring the south pole of the magnet towards the coil.
•  Move the magnet with a larger speed towards the coil. The pointer of the galvanometer deflects more. The deflection of the pointer in the galvanometer increases as the speed of the magnet increases.
• Deflection of the pointer in the galvanometer happens due to the relative motion of the coil and magnet. Relative motion between the magnet and coil induces an electric current on the coil with a galvanometer.
• When we bring the magnet towards the coil, the magnetic flux through the coil increases. It causes emf in the coil. Current induces in the coil. When we bring the magnet away from the coil, the magnetic flux through the coil decreases. It causes emf in the coil. Current induces in the coil. The current direction will be different when we move the magnet toward and away from the coil.

Experiment II

Case - 1 - When coil C2 moves towards or away from coil C1

• Replace the magnet with coil C2, which is connected to the battery (Fig 2). The pointer in the galvanometer deflects when coil C2 moves towards or away from coil C1. Deflection of the pointer in the galvanometer happens when we move the coil C1 or coil C2
• Relative motion between coils induces an electric current on the coil  C1 with the galvanometer.

Fig 2: Current is induced in coil C1 due to the motion of the current carrying coil C2

• When we move coil C2 towards coil C1, the magnetic flux through coil C1 increases. It causes emf in coil C1. Current induces in the coil C1.
• When we move coil C2 away from the coil, the magnetic flux through coil C1 decreases. It causes emf in the coil. Current induces in the coil.
• The direction of the current will be different when we move coil C2 towards and away from coil C1

Case - 2 -  When the key closes and opens

In this experiment, coil C2 is connected to the battery through the key (Fig 3). Coil C2 is placed very close to coil C1

Fig 3: Current is induced in coil C1 when we close the key and open the key

• The pointer in the galvanometer deflects when we close the key and open the key. The direction of deflection of the pointer in the galvanometer is different when the key is closed and when the key is opened.
• When we close the key, the current increases from 0 to the maximum value. Current through the coil C2 Increases. The magnetic field through coil C2 increases. It causes emf in coil C1. Current induces in the coil C1.
• When we open the key current through C2, it decreases from the maximum to the 0 value.  The magnetic field through coil C2 decreases. It causes emf in coil C1. Current induces in coil C1.
• The current direction on coil C1 is different when the key is closed and when the key is opened.

Case - 3 - Changing current through coil C2

• You can repeat the experiment by connecting the coil C2 through rheostat. Vary the current by moving the slider of the rheostat. (Fig 4)
• The pointer in the galvanometer deflects when we vary current through coil C2. The direction of deflection of the pointer in the galvanometer will be different when we increase and decrease the current.
• When current through coil C2 changes, the magnetic field through coil C1 changes. It causes emf in coil C1.

Fig 4: Current is induced in C1 when we move the slider of the rheostat

Case - 4 - Changing the common area between the coils

• You can repeat the experiment by changing the common area between the coils C1 and C2.
• The pointer in the galvanometer deflects when we change the common area between the coils C1 and C2. The direction of deflection of the pointer in the galvanometer will be different when we increase and decrease the common area between the coils.
• When we change the common area between the coil, magnetic flux through coil C1 changes, causing emf in coil C1. It causes the current in coil C1.

Case - 5 - Induced emf by changing the angle between the magnetic field and area vector.

The Arrow coming out of the loop is the area vector whose magnitude is equal to the area of the loop and whose direction is perpendicular to the plane of the loop (Fig 5).

Fig 5: Emf is induced when we change the angle between the magnetic field and the area vector

• When the area vector is perpendicular to the magnetic field, the magnetic flux is 0. When the area vector is parallel to the magnetic field, the magnetic flux is maximum. When we rotate the loop from 90° to 0°, the magnetic flux through the loop changes, causing the induction of an emf.
• Electric generators work on the principle of electromagnetic induction. Electric generators induce current by rotating a coil in a magnetic field.

Lenz's Law

The direction of induced emf can be found using Lenz's law. (Fig 6)

Fig 6: Lenz's law

Lenz's law states that "the polarity of induced emf is such that it tends to produce a current which opposes the change in magnetic flux that produced it.”

Students