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Advanced Physics Topics like quantum mechanics and relativity have revolutionized our understanding of the universe.
State Lez’s Law Related with the Direction of Induced Current
The phenomenon of electromagnetic induction is completely described by three laws. The exact informations obtained from these laws are:
- Whether or not an emf would be induced in a coil (Fara-day’s 1st law).
- The magnitude of this induced emf (Faraday’s 2nd law).
- The direction of the induced emf (Lenz’s law)
Faraday’s Laws
First law Whenever the magnetic flux linked with a coil changes with time, an electromotive force is induced in the coil. Induced emf lasts as long as the magnetic flux linked with the coil continues to change.
Second law: The magnitude of the induced emf is directly proportional to the time rate of change of magnetic flux linked with the coil.
If the change in magnetic flux linked with a coil in time dt be dϕ, according to Faraday’s second law,
induced emf, e ∝ \(\frac{d \phi}{d t}\) ………. (1)
Explanation of Faraday’s two laws: in Fig., the magnetic lines of force or lines of induction adjacent to the north-pole (IV) of a bar magnet M are shown.
Explanation of the first law:
In Fig., if a closed coil be moved from A to A’ or from A’ to A, the number of lines of force through that coil, i.e., magnetic flux linked with it decreases or increases, respectively. According to Faraday’s first law, during the motion of the coil in both the cases an emf will be induced in the coil. On the other hand, if the coil is at rest, no change in the magnetic flux will occur and hence induction will not take place. From the experiment of electromagnetic induction, the same result is obtained. So, from the first law, the cause of the electromagnetic induction and the time of existence of the induced emf can be ascertained.
Explanation of the second law: If the relative velocity between the coil and the magnet is increased, the strength of induced emf also increases. This phenomenon is in accordance with Faraday’s second law, because if the coil is moved quickly, the rate of change of the number of lines of force, i.e., the rate of change of magnetic flux also increases. So, the second law determines the magnitude of the induced emf.
Lenz’s Law
From Faraday’s laws, the direction of the induced emf cannot be ascertained. The necessary law for the determination of this direction is Lenz’s law. This may be called the third law of electromagnetic induction.
Statement: In case of electromagnetic induction, the direction of the induced emf is such that, it always opposes the cause of induction in the circuit.
Explanation of Lenz’s law:
Relative motion between a magnet and a closed coil: Let C be a circular conducting coil [Fig.]. Along its axis, the north pole (IV) of a bar magnet M is moved towards the coil. According to Lenz’s law, the induced current in C will oppose the motion of the magnet M, i.e., it will repel the magnet. For this, a north pole would be generated on the front face of the coil. So, if viewed from the side of the magnet, the induced current will be anticlockwise. Similarly, if the magnet is moved in the opposite direction, the current in the coil C will be clockwise.
In Fig., if the magnet M is moved forward beyond the surface of the coil C, the induced current in the coil will attract the south pole S of the magnet. Hence, a north pole should be generated on the back- face of the coil and a south pole on the front-face. So, if viewed from the front-face, the induced current is clockwise.
Primary and secondary coils: in Fig., let a current be passed through the primary coil P by switching on the circuit. At that moment, the instantaneous effect on the secondary coil becomes similar to the effect due to a sudden rapid movement of a current carrying coil towards the secondary coil. So, according to Lenz’s law, the induced current in the secondary coil S will repel the primary coil.
Since, two unlike parallel currents repel each other, we can conclude that, the induced current in the secondary coil is opposite in direction with respect to the primary coil. On the other hand, if the primary circuit is switched ‘off’, just at that moment, a like current will be induced in the secondary coil.
Falling of a magnet through a coil: when a body is allowed to fall freely in the gravitational field of earth, it falls with acceleration due to gravity (g). Let us consider a closed circular coil C kept horizontally and along its axis a bar magnet M is released [Fig.]. Due to downward motion of the magnet, an induced current is set up in the coil C.
According to Lenz’s law, the direction of this induced current will be such that, the downward motion of the magnet will be opposed. As a result, the magnet will fall with a smaller acceleration than that due to gravity (g). If the coil is replaced by a long cylindrical conductor (say, a copper pipe), the slower motion of the magnet becomes more clearly noticeable.
Lenz’s law from the law of conservation of energy:
Let a bar magnet M be moving towards a closed coil C along its axis [Fig.]. Its north pole faces the coil. As a result, a current is induced in the coil, i.e., electrical energy is developed. According to the law of conservation of energy, this electrical energy can only be obtained at the cost of other forms of energy and hence some external positive work is to be done against an opposing force.
The current induced in the coil is the source of this opposing force. Naturally, the direction of the induced current has to be anticlockwise to develop an N pole in its front face which will oppose the motion of the bar magnet. So, Lenz’s law is a natural consequence of the law of conservation of energy.
Law of conservation of energy from Lenz’s law:
According to Lenz’s law, the direction of the induced emf is such that, this induced emf can oppose the cause of generation of electric current in the circuit. It means that, if we gradually bring a magnet near the coil, the induced emf will oppose the forward motion, and when the magnet is taken away from the coil, it opposes that receding motion. As a result, to generate relative motion between the magnet and the coil, some work must be done against this opposing force and this work done will induce electromotive force obeying the principle of conservation of energy. Hence, the principle of conservation of energy can be obtained from Lenz’s law.