Question

derive an expression for the force as per the unit length between two parallel conductor carrying current plz help in a easy way to write​

Answer 1

Force per unit length between two long straight parallel conductors: Suppose two long thin straight conductors (or wires) PQ and RS are placed parallel to each other in vacuum (or air) carrying currents I1 and I2 respectively. It has been observed experimentally that when the currents in the wire are in the same direction, they experience an attractive force (fig. a) and when they carry currents in opposite directions, they experience a repulsive force (fig. b). Let the conductors PQ and RS carry currents I1 and I2 in same direction and placed at separation r. (fig.). Consider a current–element ‘ab’ of length ΔL of wire RS. The magnetic field produced by current-carrying conductor PQ at the location of other wire RS According to Maxwell’s right hand rule or right hand palm rule no. 1, the direction of B1 will be perpendicular to the plane of paper and directed downward. Due to this magnetic field, each element of other wire experiences a force. The direction of current element is perpendicular to the magnetic field; therefore the magnetic force on element ab of length ΔL According to Fleming’s left hand rule, the direction of magnetic force will be towards PQ i.e. the force will be attractive. On the other hand if the currents I1 and I2 in wires are in opposite directions, the force will be repulsive. The magnitude of force in each case remains the same.

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