Describe the working principle of a moving coil galvanometer. Why is it necessary to use (i) a radial magnetic field and (ii) a cylindrical soft iron core in a galvanometer? Write the expression for current sensitivity of the galvanometer.

Can a galvanometer as such be used for measuring the current? Explain.

OR

A. Define the term ‘self-inductance’ and write its S.I. unit.

B. Obtain the expression for the mutual inductance of two long co-axial solenoids and would one over the other, each of length L and radii and and and number of turns per unit length, when a current I is set up in the outer solenoid

a) The moving coil galvanometer works on the principle that a current carrying loop experiences a torque when placed in external magnetic field. The Moving coil galvanometer consists of a coil having large number of turns, which is allowed to rotate about a fixed axis, in a uniform radial magnetic field. Radial magnetic field is used as it ensures that maximum torque is applied to the coil at all angles and there is a cylindrical soft iron core which not only makes the field radial but also increases the strength of the magnetic field. When a current flows through the coil, a torque acts on it.

This torque is given by.

=NIAB

N is the number of turns, I is the current, A is area of c.s., B is the strength of the magnetic field.

The magnetic torque NIAB tends to rotate the coil. A spring S_P provides a counter torque k that balances the magnetic torque NIAB, resulting in a steady angular deflection . In equilibrium,

k= NI AB

where k is the torsional constant of the spring, i.e. the restoring torque per unit twist. The deflection is indicated on the scale by a pointer attached to the spring. We have.

The term NAB/k is constant for a given galvanometer and is referred to as current sensitivity, i.e.,

No a galvanometer cannot be used to measure current as such because it is highly sensitive to even slight fluctuation in current. If such a large values of current can destroy the galvanometer.

OR

i) When an EMF is induced in a single isolated coil due to change of flux through the coil by the virtue of the varying current through the same coil is called Self Induction. In this case, flux linkage through a coil of N turns is proportional to the current through the coil and is expressed as,

Where, L is called self-inductance of the coil. The SI unit of self-inductance is Henry (H).

ii) Given: -

Two long co-axial solenoids each of length l. The radius of the inner solenoid S₁ by r₁ and the number of turns per unit length by n₁. The same physical quantities for the outer solenoid S₂ are r₂ and n₂, respectively. Let N₁ and N₂ be the total number of turns of coils S₂ and S₂, respectively.

Derivation: -

When a current I₂ starts to flow in S₂, it in turn sets up a magnetic flux through S₁. Let us denote it by F₁. The corresponding flux linkage with solenoid S₁ is

N₁ = M₁₂I₂ ….(a)

The mutual inductance of solenoid S₁ with respect to solenoid S₂ is known as M₁₂. The magnetic field due to the current I₂ in S₂ is,

B = μ₀n₂I₂

The resulting flux linkage with coil S₁ is,

N₁ = (n₁l) (r₁²) (n₂I₂)

N₁ = n₁n₂ r₁²l I₂

where the total number of turns in solenoid S₁ is denoted n₁l. Thus, from Eq. (a), we can write,

Conclusion: -

The mutual inductance is