Principles of Meter Bridge and Ampere's Circuital Law
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The Meter Bridge
The Meter Bridge consists of a wire of length 1 m and of uniform cross-sectional area stretched taut and clamped between two thick metallic strips bent at right angles, as shown. The metallic strip has two gaps across which resistors can be connected. The end points where the wire is clamped are connected to a cell through a key. One end of a galvanometer is connected to the metallic strip midway between the two gaps. The other end of the galvanometer is connected to a 'jockey'. The jockey is essentially a metallic rod whose one end has a knife-edge which can slide over the wire to make an electrical connection.
The Potentiometer
The Potentiometer is a versatile instrument. It is basically a long piece of uniform wire, sometimes a few meters in length, across which a standard cell is connected. In actual design, the wire is sometimes cut into several pieces placed side by side and connected at the ends by thick metal strips. The wires run from A to C. The small vertical portions are the thick metal strips connecting the various sections of the wire. A current I flows through the wire which can be varied by a variable resistance (rheostat, R) in the circuit. Since the wire is uniform, the potential difference between A and any point at a distance l from A is εφ = ll.
Ampere's Circuital Law
There is an alternative and appealing way in which the Biot-Savart law may be expressed. Ampere’s circuital law considers an open surface with a boundary. The surface has current passing through it. We consider the boundary to be made up of a number of small line elements. Consider one such element of length dl. We take the value of the tangential component of the magnetic field, Bt, at this element and multiply it by the length of that element dl [Note: Bt dl = B · dl]. All such products are added together. We consider the limit as the lengths of elements get smaller and their number gets larger. The sum then tends to an integral. Ampere’s law states that this integral is equal to μ₀ times the total current passing through the surface.