MOVING COIL GALVANOMETER

Galvanometer: 

A galvanometer is a device to detect current in a circuit. 

Principle: 

A current carrying coil placed in a magnetic field experiences a current dependent torque, which tends to rotate the coil and produces angular deflection. 

Construction:

A galvanometer consists f a rectangular coil of fine insulated copper wire wound on a light non magnetic metallic frame. The two ends of the axle of this frame are pivoted between two bearings. The motion of the coil is controlled by a pair of hair springs of phosphor bronze. The inner ends of the springs are soldered to the two ends of the coil and the outer ends are connected to the the binding screws. The springs provide the restoring torque and serve as current leads. A light aluminium pointer attached to the coil measures its deflection on a suitable scale. 

The coil is symmetrically placed between the cylindrical pole pieces of strong permanent horseshoe magnet. 

Theory and Working:

Let Ｉ = current flowing through the coil PQRS

     a, b = sides of the coil PQRS

       A  = ab = area of the coil

       θ = angle between the direction of B and normal to the plane of the coil.

       N = number of turns in the coil

Since the field is radial, the plane of the coil always remains parallel to the field B. Magnetic forces on the sides QR and SP are equal, opposite and collinear, so their resultant is zero. According to Fleming's left hand rule, the side PQ experiences a normal inward force equal to NＩbB why is the side QR experiences an equal normal out what force. The two forces on sides PQ and RS are equal and opposite. They form a couple and exert a torque given by 

τ = one of the force x perpendicular distance between them 

τ = F a sin θ = ＩbBa sin θ = ＩBA sin θ

[ ∵ ab = A]

If the rectangular loop has N turns, the torque increases N times ie.,

τ = NＩBA sin 90° = NＩBA

Here, θ = 90°, because the normal to the plane of coil remains perpendicular to the field B in all positions. 

The torque τ deflects the coil through an angle α. A restoring torque is set up in the coil due to elasticity of the springs such that

      τᵣ ∝ α   or   τᵣ = kα 

Where K is is the the torsion constant of the springs. 

Restoring Torque = Deflecting Torque

kα = NＩBA

Or  α = (NBA/k)Ｉ

Or      α ∝ Ｉ

Thus the deflection produced in the galvanometer coil is proportional to the current flowing through it. Consequently, the instrument can be provided with a scale with equal divisions along a circular scale to indicate equal steps in current. Such a scale is called linear scale.

Ｉ = (k/NBA) α = Ｉ = Gα

G = (k/NBA) is constant for a galvanometer and is called galvanometer constant for current reduction factor of the galvanometer.

TORQUE EXPERIENCED BY A CURRENT LOOP IN A UNIFORM MAGNETIC FIELD

Torque on a current loop in a uniform magnetic field:

A rectangular coil PQRS suspended in a uniform magnetic field B. The axis of the rectangular coil is perpendicular to the field. 

Let Ｉ = current flowing through the coil PQRS

     a, b = sides of the coil PQRS

       A  = ab = area of the coil

       θ = angle between the direction of B and normal to the plane of the coil.

 

Direction of the area and B makes an angle θ

all the forces acting on the sides of the rectangular coil PQRS

According to Fleming's left hand rule, 

i) the magnetic force on the side QR is F₁

 and it is acting upward.

F₁ = Ｉ(a xB) = ＩaB

ii) the magnetic force on the side SP is F'₁ and it is acting downward. 

F'₁ = Ｉ(a xB) = ＩaB

So, net force along vertical direction is zero as 

F₁ and F'₁ are equal and opposite as both are acting along the axis of the coil.

iii) the magnetic force on the side SR is F and it is coming out of the board.

F = Ｉ(b xB) = ＩbB

iv) the magnetic force on the side QP is F' and it is going into the board.

F' = Ｉ(b xB) = ＩbB

coil as seen from the top : m is the direction of the magnetic moment as well as coil area (perpendicular to the plane of the coil).

Therefore F and F' will produce a torque τ

We know, 

τ = one of the force x perpendicular distance between them 

τ = F a sin θ = ＩbBa sin θ = ＩBA sin θ

[ ∵ ab = A]

If the rectangular loop has N turns, the torque increases N times ie.,

τ = NＩBA sin θ

But there is one physical quantity called "magnetic moment" or m = NＩA

τ = m B sin θ = m x B

The direction of the torque τ is such that it rotates the loop clockwise about the axis of the loop. 

The torque will be zero when θ = 0 ie., When the plane of the loop is perpendicular to the magnetic field. 

The torque will be maximum when θ = π/2 and τ = NＩBA ie., when the plane of the loop is parallel to the magnetic field.