Electromagnetic Induction and Lenz's Law

Faraday Laws of electromagnetic induction:

First law of faraday’s of electromagnetic induction:

It state that whenever is a change in the magnetic flux lined with a coil an emf is induced in a coil which lasts so long as the change in magnetic flux continues.

Second law of faraday’s of electromagnetic induction:

This law give the measurement of induce emf. a/c to this law the magnitude of emf induce in a is proportional to the rate of change of magnetic flux linked with it i.e.

Induced emf e α dɸ/dt

Therefore e=-k dϕdt

Where k is called proportionality constant whose value is 1 and

Negative sign show the opposing nature of the induce emf so the above expression may be written as e=-dϕdt

Let at time t=0 second fluxed with a coil is ɸ1 and after time t=t second flux linked ɸ2 then change in fluxed link is given by ɸ2- ɸ1=dɸ

Therefore induced emf (e)=-dϕt

Lenz's law:

According to Lenz's law, the direction of induced current in a coil is such that it always opposes the cause which produces it. This law follows the law of conservation of energy i.e. Energy neither can be created nor can be destroyed but can change from one form to another. In lenz’s law when the magnet is moved towards or away from coil, emf is induced in the coil at the expense of mechanical energy spent by the external agent. Hence in this way mechanical energy is converted to electrical energy. This show the Lenz's law is in accordance with the law of conservation of energy.

Production of E.M.F:

The induced emf can be produced by the following ways

By rotating coil in a magnetic field

By rotating rod in the magnetic field perpendicular to the length and the magnetic field

By passing a alternating current in the coil (self induction)

By mutual induction (passing current in the neighboring coil)

E direction of the emf can be determined by two ways

i. Lenz law: According to Lenz's law, the direction of induced current in a coil is such that it always opposes the cause which produces it. Consider the magnet which is brought towards the coil due to which flux linked with the coil changes .this causes the induced emf in the coil and induced current flows in a circuit as shown in a fig.

thus obtained current produces magnetic field in the coil with the north pole at the left and south pole at the right end .the north pole of the coil repels the north pole of the magnet opposing the motion of the magnet so that work is to be done to move further towards the coil. Similarly if the magnet is taken away from the coil the south pole of the magnet attracts the North Pole and work is to be done against the attractive force .In this way direction of the induced emf can be obtained from the receding motion of the magnet.

ii. Fleming right hand rule: When a conductor such as a wire attached to a circuit moves through a magnetic field, an electric current is induced in the wire due to Faraday's law of induction. The current in the wire can have two possible directions. Fleming's right-hand rule gives which direction the current flows

The right hand is held with the thumb, first finger and second finger mutually perpendicular to each other (at right angles), as shown in the diagram.

The thumb is pointed in the direction of motion of the conductor.

The first finger is pointed in the direction of the magnetic field. (North to south)

Then the second finger represents the direction of the induced or generated current (the direction of the induced current will be the direction of conventional current; from positive to negative)