EXPERIMENT : Determintion of moment of magnet by measuring field at points along the axis of a current carrying coil

   AIM

To study the field at a point along the axis of a current carrying circular coil   and  hence  to find moment of magnet

APPARATUS REQUIRED

Circular coil apparatus, compass box, rheostat, battery or power supply, ammeter, commutator, key and connecting wires.

FORMULA USED

 Field at a point along the axis of the coil is,

             nia² 

  F = ^___________      ampere/metre 

          2(a² + x²)^3/2

Where,

n -Number of turns in the coil 

i -current measued (A)

a -Radius of the coil (m)

x - distance between centre of coil and  centre of compass box (m)

Moment of magnet is,

                                                      𝜋nia2𝜇0(d2-l2)2

                                      M =   __________________        weber.metre

                                                         d(a2 + x2)3/2

Substituting F and 𝜇0 , we can reframe the equation as,

                                                  8𝜋2F(d2-l2)2

                                      M =   ____________ x 10-7       weber.metre

                                                         d

Where,

𝜇0 -Permittivity of free  space =4𝜋 x 10-7 Henry/metre

 l -semilength of magnet (m)

d- distance between centre of compass box and centre of bar magnet   (m)

CIRCUIT DIAGRAM

Figure 1: Circuit to find the field at points along
 the axis of the coil

PROCEDURE

The preliminary adjustments are carried out as follows

Figure 2: Circular coil apparatus with compass box 

• The leveling screws are adjusted so that the circular coil is vertical.

• The wooden bench is adjusted to be along the magnetic east-west direction

• A compass box is placed with its centre coinciding with the axis of the coil

• The compass box alone is rotated till the aluminium pointer reads 0° − 0°

                Electrical connections are made as shown in the circuit diagram (figure 1). The compass box is placed along its axis, with its centre at a distance x from the centre of the coil on one side. A suitable current (say, 1A) is passed through the coil by adjusting rheostat so that the deflection of the aluminium pointer lies between 30 º and 60 º. Two readings θ1 and θ2 corresponding to two ends of the pointer are noted. Now a bar magnet is placed along the axis of coil at a distance d1 from the centre of compass  box to make deflection 0-0 (as shown in figure 3).

Figure3: method to nulify the deflection using a magnet

    

        Now the direction of the current is reversed using commutator, two more readings θ3 and θ4 are

noted. The opposite pole of the magnet  at a distance d2 from the centre of compass  box  makes the

deflection 0-0. The experiment is repeated for another value of current,  keeping the compass box at the

same distance x.

OBSERVATION

Number of turns in the coil n= 30 turns

Circumference of the coil (2πa) = 45 cm

Radius of the coil a =0.073m

semilength of the magnet=0.038m

                                                                                                            Mean (M)= 1.7936 x10^-6  wm

Result:

i)The field at points along the axis of a current carrying circular coil is studied.

ii)The value of moment of magnet is  1.7936 x10^-6  wm