To study variation of magnetic field with distance on the axis of a circular coil carrying current

Aim

To study variation of magnetic field with distance on the axis of a circular coil carrying current

Apparatus Required:

Stewart Gee type galvanometer, battery plug key, commutator, rheostat and ammeter.

Description:-

Stewart and Gee galvanometer is shown above. Its construction resembles that of tangent galvanometer and deflection magnetometer. It consists of a circular coil in a vertical plane fixed to a horizontal bench at its middle point. The ends of the coil are connected to binding screws. A magnetic compass box is arranged such that it can be sided along a horizontal scale passing through the center of the coil. The length of the scale is perpendicular to the plane of the coil. The compass box consists of a short magnetic needle and a long aluminum pointer attached at its midpoint perpendicular to it and they are pivoted at the center of a horizontal circular scale graduated in diagrams. The circular scale consists of four quadrants each of which measures angles from 0 degree to 90 degree. A plane mirror is provided below the pointer so that the deflections can be provided without parallax.

Procedure:

1. The circuit is constructed as shown in fig. The primary adjustments of the instrument are made.
2. The coil of the instrument is set along the magnetic meridian. The aluminum pointer is made to read 00 - 00 with no current. The ends of the coil are connected to the commutator and through it to the battery rheostat and ammeter.
3. When the circuit is closed with the plug key, a current flows through the circular coil. A magnetic field is produced on the axis of the coil.
4. The magnetic needle in the compass is subjected to the horizontal component earth's magnetic field (H) and magnetic field (F) due to the circular coil carrying current. Those two magnetic fields are acting at right angles to each other.
5. The magnetic needle dings along the direction of resultant magnetic field. The magnetic needle is deflected through an angle θ from the direction of (H) the Horizontal component of earth's magnetic field. Then we get the equation
B = BH tan ?
6. The current in the circuit is adjusted such that the deflection lies between 30 degree to 60 degree using the rheostat.
7. The compass box is displaced by 5cm or 10cm along the horizontal seal of the deflection of the needle is measured at every distance by reading both ends of the pointer. Let the readings be θ1 and θ2. The readings θ3 and θ4 are observed after reversing the direction of current.
8. The experiment is repeated for points on the other side of the coil. If θ is the average of the four deflection readings tan θ α B.
9. A graph is drawn with tan θ along x-axis. This graph shows the variation of magnetic field on the axis of circular coil with distance. It is symmetrical about y-axis and the magnetic field is maximum at the center of the coil.

Formula:The magnetic field B at a point on the axis of a circular coil of a turns and radius a is given by the equation

Where I = current passing through the coil

X = distance of the point from the center of the coil.

Observations:

BH = 0.38x10 ^-4Tesla

μ0 = 4πX10 ⁷

Current I =----------amp.

n= …..

The values of F calculated from equation B = B _Htan θ and should be equal.

B =μ0nia²/2(x ²+ α ²) ^3/2