# Faraday’s Law of Electromagnetic Induction

Faraday’s Law states that, whenever the flux of magnetic field through the area bounded by a closed conducting loop changes, an emf is produced in the loop. The produced emf is given by

ξ = -dØ/dt
where Ø = ∫B.ds is the flux of the magnetic field through the area. Ø is called the magnetic flux.

It is the law of electromagnetic induction.The SI unit of magnetic flux is Weber which is equivalent to Tesla meter2Faraday’s Law is basically an experimental result. Faraday performed a sequence of experiments to arrive at the result mentioned above. We will discuss the experiment to better understand how emf is produced due to changing magnetic flux.

Material Required: Conducting Loop, Bar Magnet and Galvanometer

A conduction loop is connected to the Galvanometer and the Bar Magnet is slowly brought toward the loop along the axis of the loop. Now the bar magnet is taken away from the loop but again along the axis of the loop. Please perform the following steps from the simulator below. Be sure to tick the the field lines checkbox in the simulator below.

• Take the bar magnet closer to the coil.
• Take the bar magnet away from the coil.
• Hold the bar magnet stationary.

#### Observations:

• As the bar magnet is brought nearer to the loop, there is a deflection in the Galvanometer needle. This means that a current is flowing in the loop in a particular direction as shown by the deflection of Galvanometer. But current can only flow if there is some emf. This means that there must have been some induced emf due to movement of bar magnet.
• As the bar magnet is taken away from the loop, again there is a deflection in the Galvanometer needle but this time in opposite direction. What does this mean? This means that current flowing in the loop is in opposite direction. Thus the direction or polarity of emf changed which caused the flow of current in opposite direction.
• When the bar magnet is held stationary, there is no deflection in the needle of Galvanometer.

#### Conclusion and formulation of Faraday’s Law

Thus we have these three observations and we need to formulate how Faraday came to a conclusion.  See, as we bring the bar magnet toward the conducting loop, the strength of magnetic field increases. But does this mean that induced emf depend on strength of magnetic field alone? No, because we saw in experiment that when the bar magnet is held stationary near the loop, no current flows through the loop. Thus, the induced emf doesn’t only depend on the strength of magnetic field.

Next, when we bring the bar magnet faster toward or away from the loop, the magnitude of deflection of Galvanometer increases. Well, this means induced emf depends on the rate of change of magnetic field passing through the conducting loop. Mind the word magnetic field passing through the loop. Thus more the number of magnetic field lines passing through the loop, more will be the magnitude of induced emf. Actually this is the magnetic flux. Magnetic flux is the number of magnetic field lines passing through a closed curve.

Therefore, we can now say that induced emf depends on the rate of change of magnetic flux linking the conducting loop. What about the negative sign?

From observation (1) and (2), we can at least say that the induced emf is directional in nature and depends on whether the flux linkage through the loop is increasing or decreasing. The significance of this negative sign is explained by Lenz in his famous Lenz’s Law.

#### Summery

Thus to summarize, as per Faraday’s Law the induced emf is dependent on rate of change of flux linking through a conducting coil or loop. Therefore, to have an induced emf the flux through the coil must change.

As Magnetic Flux Ø = B.A where bold sign means vector form. Thus flux can be changed by varying the following:

• Cross sectional area of the coil.
• Magnitude or direction of magnetic field.
• Both the cross sectional area and magnetic field.

Hope you fully understood the Faraday’s Law. If still you have any doubt, please write in comment box. Thank you!