According to the Lenz's law, the direction of induced current in a closed circuit is always such as to oppose the cause that produces it. Say, a magnet moving towards a conducting coil is inducing a current in the coil. This means the movement of the magnet has created electrical energy in the conducting coil. According to the conservation of energy, this electrical energy has to be produced from some other form of energy. This other form of energy is nothing but the kinetic energy of the magnet. Therefore, as current is produced in the coil, the magnet slows down or in other words, it gets opposed by the induced current.

Inductance is a property of a coil which opposes the change in current flowing through it. Inductance depends only on the geometry of the coil. It is a scalar quantity and its SI unit is henry.

Obtain an expression for the mutual inductance of two long co-axial solenoids.

Consider two long co-axial solenoids S 1 and S 2 of radii r 1 and r 2 . Let the number of turns in the solenoids be N 1 and N 2 and number of turns per unit length be n 1 and n 2 . When a current I 2 is set up through S 2 , it sets up a magnetic flux through S 1 . The corresponding flux linkage with solenoid S 1 : N 1 φ 1 = M 12 I 2 ...(i) M 12 is called the mutual inductance of solenoid S 1 with respect to solenoid S 2 . The magnetic field due to the current I 2 in S 2 is μ 0 n 2 I 2 . Hence, the flux linkage: N 1 φ 1 = n 1 l π r 1 2 μ 0 n 2 I 2 = μ 0 n 1 n 2 π r 1 2 l I 2 ....(ii) On comparing (i) and(ii), we get: M 12 = μ 0 n 1 n 2 π r 1 2 l ....(iii) (iii) is the expression for the mutual inductance. Edge effects are neglected and the magnetic field inside the solenoid is taken as uniform because the solenoids are considered very long.

Describe the ways in which Eddy currents are used to advantage.

When bulk pieces of conductors are subjected to changing magnetic flux, induced currents produced in them are called eddy currents. The eddy currents can be used to advantage in the following ways: (i) Magnetic braking in trains: Strong electromagnets are situated above the rails in electrically powered trains. When electromagnets are activated, the eddy currents induced in the rails oppose the motion of the train. As there are no mechanical linkages, the braking effect is smooth. (ii) Electromagnetic damping: Moving coil galvanometers have a fixed core made of nonmagnetic metallic material. When the coil oscillates, the eddy currents generated in the core oppose the motion and bring the coil to rest quickly. (iii) Induction furnace: It can be used to produce high temperatures and can be utilised to prepare alloys by melting the constituent metals. A high frequency alternating current is passed through a coil which surrounds the metal to be melted. The eddy currents generated in the metals produce high temperatures sufficient to melt. (iv) Electric power meters: A metal disc is present inside it. Electric currents are induced in it, and it rotates in a magnetic field induced by the alternating current in the coil.

According to the Lenz's law, the direction of induced current in a closed circuit is always such as to oppose the cause that produces it. Say, a magnet moving towards a conducting coil is inducing a current in the coil. This means the movement of the magnet has created electrical energy in the conducting coil. According to the conservation of energy, this electrical energy has to be produced from some other form of energy. This other form of energy is nothing but the kinetic energy of the magnet. Therefore, as current is produced in the coil, the magnet slows down or in other words, it gets opposed by the induced current.