**Magnetism Moving Coil Galvanometer**

**Torque on a current carrying loop suspended freely in a magnetic field.**

When a loop is suspended freely in a magnetic field and a current is passed through it, we find that the resultant force on the loop is zero but the resultant torque is not zero.

Suppose, at any instant during the rotation of the loop normal drawn on the plane of loop or axis of the loop makes an angle θ with the direction of magnetic field. Hence moment of couple at this instant is given by

T = Force F_{1} × Perpendicular distance

= ilB × b sin θ

= i(l × b) B sin θ

**T = iAB sin θ **

Where A = l × b = area of the current loop.

**Important points**

The above formula for torque is valid for any shape of closed loop i.e., circular and rectangular or any other. This can be easily justified by considering any loop to be divided into a large number of small adjacent rectangular loops.

If instead of a single current loop, we have a coil or solenoid consisting of large number of loops, then a couple of lAB sin θ will act on each loop. Thus, the torque or couple acting on a coil consisting of N turns is given by

T = NlAB sin θ

**T = NlA × B = M × B**

Where M = NlA = magnetic dipole moment of the current carrying coil.

Torque will be minimum = 0 when sin θ = min = 0, i.e., θ = 0˚ or 180˚ the place of the coil is perpendicular to magnetic field, i.e., normal to the coil is perpendicular to the field.

Torque will be maximum when sin θ = max = 1. i.e., θ = 90˚, i.e., normal to the coil is perpendicular to the field.

By analogy with electric or magnetic dipole in a field, in case of a current carrying coil in a field.

U = – M.B

W = MB (1 – cos θ)

Instruments such as electric motor, moving coil galvanometer and tangent galvanometers are based on the fact that a current carrying coil in a uniform magnetic field experiences a torque.

**Moving Coil Galvanometer:**

In case of a moving coil galvanometer the deflecting torque due to current in the coil BiNA (by making the field radial θ become 90˚) is balanced by the restoring couple due to elasticity of spring supporting the coil. So, if C is the restoring couple per unit twist and φ is the direction of the coil;

**BiNA = C φ**

Where, (K = C/NAB) is a constant for a given galvanometer called as Reduction factor of the galvanometer.

In this expression, N = number of turns in the coil, A = area per turn of the coil, B = magnetic induction of the radial magnetic field.

Elastic torsional constant C depends upon the three factors: 1. Modulus of rigidity of the material of suspension strip η. 2. Length of the suspension strip and. 3. radius of suspension strip. The dependence on above three factors is according to relation

**C = π ηr ^{4}/2l**

Sensitivity – sensitivity of a galvanometer can be expressed as

**S = φ/I = 1/K = NAB/C**

Higher is deflection produced in galvanometer even for a very small current, more sensitive is the galvanometer, ie higher is the value of (φ/i) higher will be the sensitivity of the galvanometer.

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