Define self inductance and write its Si unit. Derive an expression for self inductance of a long solenoid of length l , cross sectional area A having N number of turns.

The self-inductance of a coil is defined as the induced emf set up in the coil when the current through it changes at the unit rate. SI unit of self-inductance is henry ( H ) Consider a long air solenoid having N number of turns. If the current in the solenoid is I , then the magnetic field within the solenoid B = μ 0 N l I Where μ 0 = 4 π × 10 - 7 H m - 1 is the permeability of free space. Area of the cross-section of solenoid A = π r 2 Flux linked with solenoid ϕ = N B A = N μ 0 N l I π r 2 = μ 0 N 2 π r 2 I l Self-inductance of the coil L = ϕ I = μ 0 N 2 π r 2 l ∴ Self-inductance of the coil L = μ 0 N 2 π r 2 l If the core has a relative permeability μ r Self-inductance L = μ 0 μ r N 2 π r 2 l

The electric current flowing in a wire from P to Q is decreasing. Find out the direction of the induced current in the metallic loop kept above the wire as shown in the figure.

According to the right hand rule the current in wire will produce a magnetic field vertically downward near the coil . When the current in wire BA decreases, according to Lenz's law, the current induced in the coil will be in clockwise direction. Because as a clockwise current flows in the coil the magnetic field produced in its vicinity will be in the same direction as that of the magnetic field due to the current carrying straight wire. Note: Lenz's law states that the current induced in a conductor opposes its very cause of origin. As the current induced in the coil is due to decreasing current (magnetic field will also decrease) in the straight wire, the induced current will produce the magnetic field which will oppose the decrease in magnetic field.

Draw an neat labelled diagram of an a.c. generator.

An AC generator works on the principle of electromagnetic induction. The mechanical energy is converted to electrical energy. The labelled diagram of AC generator is given below: