^Neutral points

Neutral points are the positions where the magnetic field of a magnet is completely neutralised by the horizontal component of earth’s magnetic field. The position & number of neutral points depends upon the position of magnet.

If a magnet is placed vertically as shown then we get only one neutral point situated at point L at left side of magnet if magnet’s north is down. On reversing the magnet neutral point will be at right side of magnet at point R.

Consider a magnet of dipole moment M, length 2L placed horizontally. Following drawings show the top view of the situation

 Horizontal component of earth’s field is towards . When the magnet’s north (n) is towards earth’s south (S), then magnetic field of the magnet will be towards opposite to that of B_H & both get cancelled at a point somewhere on the axial line of magnet & thus two neutral points (shown by cross marks) are obtained on the axial line (i.e. towards geographic north south line). If neutral points are situated at distance r from the centre of the magnet then at these points we can write

On reversing the magnet i.e. when magnet’s north (n) is towards earth’s north (N), two neutral points are obtained on the equatorial line (i.e. towards east – west line). At these points we can write

At balanced state

1. current in the galvanometer arm I_g is zero and

2. current flowing in the mesh ABCD is

3. Potential drop across AB is V = IR_p

4. Potential gradient K = V/L

5. As ξ_A is balanced against the potential drop of  length AN, thus

6. ξ_A ∝ b is called the principle of potentiometer.

7. To get the null point within the length of the  potentiometer ξ_D > ξ_A

Greater the length of the potentiometer wire (L), smaller is the potential gradient (k) & more is the balancing length (b), hence more is the accuracy. ‘k’ is independent of the emf of auxillary cell (ξ_A) but depends upon emf of driver cell (ξ_D), its internal resistance (r_D), resistance of potentiometer wire (AB) & any resistance (R) in the main circuit.