Jul 312013

Moving coil galvanometer is a device which is used to detect and measure small electric currents present in an electric circuit.


It is based on the principle that, “When a current carrying coil is placed in magnetic field, it experiences torque.”

moving-coil-galvanometer radial-field


A moving coil galvanometer consists of a rectangular coil having large number of turns winded in a non-metallic frame with a soft iron as a central ore. The coil is suspended between two concave poles of two permanent magnets with the help of phosphor-bronze strip. The strip also acts as a path of current to the coil because it is connected to the terminal ‘t1‘ of the galvanometer. Other end of the coil is connected to a light spring which exerts small restoring couple on the coil and then it is finally connected to terminal ‘t2‘. A concave mirror is attached on the strip to note the deflection of the coil by using a lamp and scale arrangement.

Working Method

When current is passed to the coil through the terminals ‘t1‘ and ‘t2‘, the coil gets deflected due to torque on it. This deflecting torque on the coil is given by, τd = BINAcosθ

Since the poles of the magnet are concave, the magnetic field is radial, i.e. θ = 0o. Therefore,
τd = BINA

As the coil gets deflected, the suspension wire gets twisted and restoring torque is developed on it. Let, k be the restoring torque per unit angle of twist for the suspension wire, then the total restoring torque for an angle θ is
τr = kθ

For the equilibrium of the coil,

Deflecting torque (τd) = Restoring torque (τr)

or, BINA = kθ

or, I = kθBNA

∴ = Gθ, where G = kBNA is a constant for galvanometer.

Hence, in moving coil galvanometer, deflection is directly proportional to current.

Jul 262013

Torque on a rectangular coilLet us consider a rectangular coil PQRS of length ‘l’ and breadth ‘b’ suspended in uniform horizontal magnetic field ‘B’. Let the plane of the coil make an angle ‘θ’ with the direction of magnetic field.

When current ‘I’ is passed through the coil, the magnetic force produced on the various arms of the coil are:

i) Force on arm PQ,

F1 = IlBsinθ
     = IlBsin90o
     = IlB
F1 is perpendicular to both l and B and is directed outwards.

ii) Force on arm QR,

F2 = IbBsinθ
∴ F2 is perpendicular to both b and B and is directed downwards.

iii) Force on arm RS,

F3 = IlBsinθ
     = IlBsin90o
     = IlB
∴ F3 is perpendicular to both l and B and is directed inwards.

iv) Force on arm SP,

F4 = IbBsinθ
∴ F4 is perpendicular to both b and B is directed upwards.

torque on a rectangular coil 2The forces F2 and F4 are equal and opposite and they pass through same line of action, so they cancel each other resulting to no torque or force on the coil.
The forces F1 and F3 are also equal and opposite but they pass through different lines of action, so they constitute couple or torque which is given by:

τ = (F1 or F3) × Arm of couple
   = IlB × bcosθ
   = IBAcosθ [∵ A = l × b]

If there are ‘N’ number of turns in the coil, then the total torque is:
   τ = N × IBAcosθ
∴ τ = BINAcosθ

Special Cases:
i) If θ = 0o, τ = BINA (maximum value)
When the plane of the coil is kept parallel to the magnetic field, torque on the coil is maximum.
ii) If θ = 90o, τ = 0 (minimum value)
When the plane of the coil is kept perpendicular to the magnetic field, torque on the coil is minimum.