Study of the Magnetic Field of the Axis of a Current Coil

To study the variation of magnetic field strength along the axis of a current-carrying circular coil using a tangent galvanometer and magnetometer.

Apparatus

Stewart and Gee’s type galvanometer, battery, ammeter, rheostat, one-way plug key, reversing key, connecting wires, and sandpaper.

Description of Stewart and Gee’s Tangent Galvanometer

This apparatus consists of a circular coil made of several turns of thin copper wire wound on a wooden frame. The coil is fixed vertically on a horizontal base. The free ends of the wire are connected to terminals provided at the base.

A deflection magnetometer is placed horizontally such that the center of its needle always lies on the axis of the coil. The magnetometer arms carry scales, allowing the distance of the needle from the center of the coil to be measured accurately with the help of an index attached to the sliding base.

Theory

The magnetic field B produced by a circular coil of radius r at a distance x from its center, when current I passes through n turns, is given by:

$\frac{{\mu_0 n I r^2}}{{2 (r^2 + x^2)^{3/2}}}$

Here, θ is the deflection of the magnetometer needle. Therefore,

$tan⁡θ∝B\tan \theta \propto B$

Thus, a graph between tan θ and x represents how the magnetic field varies along the axis of the coil.

Procedure

Arrange the apparatus so that the magnetometer arms are roughly along the east-west direction, and the needle lies at the center of the circular coil.
Set the plane of the coil vertically and parallel to the magnetic meridian using the magnetometer needle.
Rotate the compass box until the pointer lies along the 0–0 line.
Make the electrical connections as shown in the circuit diagram.
Adjust the current in the coil with the rheostat to obtain a deflection of about 75° when the magnetic needle lies in the plane of the coil.
Reverse the direction of the current and note the deflection in the opposite direction. Ensure both deflections are equal by adjusting the setup if necessary.
Slide the magnetometer box along the axis and find the position of maximum deflection — this corresponds to the point where the centers of the needle and coil coincide.
Note the readings from the magnetometer scale at both ends of the pointer. Reverse the current and repeat the readings.
Shift the magnetometer along the axis in steps of 2 cm, taking readings until the deflection reduces to about 10°.
Repeat the observations on the other side of the coil while keeping the current constant.
Plot a graph between tan θ and x for both sides of the coil to observe how the magnetic field varies with distance.

Observation and Calculations

Result

The distance between the points of inflection C and D is found to be approximately equal to the radius of the coil.

Precautions

Keep all magnets and magnetic materials away from the apparatus.
Maintain constant current throughout the experiment.
Avoid parallax errors while taking needle readings.

Viva Voce

Q1: What is the unit of the magnetic field?
Ans: The SI unit of magnetic field is Tesla (T). A smaller unit, Gauss (G), is also used.

Q2: How does a current-carrying circular coil behave?
Ans: It behaves like a magnet with one face acting as the north pole and the other as the south pole.

Q3: What is meant by the point of inflexion?
Ans: It is the point on a curve where its curvature changes direction.

Q4: Why is a magnetic needle used in a compass?
Ans: Because its ends always align along the north–south direction of the Earth’s magnetic field.