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#### Question

Derive an expression for the mutual inductance of two long co-axial solenoids of same length wound one over the other,

#### Solution

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Define the term self-inductance of a solenoid. Obtain the expression for the magnetic energy stored in an inductor of self-inductance L to build up a current I through it.

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on the axial line, distance ‘r’ from the centre of the solenoid. How does this expression compare with the axial magnetic field due to a bar magnet of magnetic moment ‘m’?

Two long coaxial insulated solenoids, S_{1} and S_{2} of equal lengths are wound one over the other as shown in the figure. A steady current "I" flow thought the inner solenoid S_{1} to the other end B, which is connected to the outer solenoid S_{2} through which the same current "I" flows in the opposite direction so as to come out at end A. If n_{1} and n_{2} are the number of turns per unit length, find the magnitude and direction of the net magnetic field at a point (i) inside on the axis and (ii) outside the combined system

Define self-inductance of a coil. Obtain an expression for the energy stored in a solenoid of self-inductance ‘L’ when the current through it grows from zero to ‘I’.

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