Force Between Two Parallel Current Carrying Conductors
Category : JEE Main & Advanced
The force on a length l of each of two long, straight, parallel wires carrying currents \[{{i}_{1}}\] and \[{{i}_{2}}\] and separated by a distance a is
\[F=\frac{{{\mu }_{0}}}{4\pi }\cdot \frac{2{{i}_{1}}{{i}_{2}}}{a}\times l\]
Hence force per unit length \[\frac{F}{l}=\frac{{{\mu }_{0}}}{4\pi }\cdot \frac{2{{i}_{1}}{{i}_{2}}}{a}\]\[\left( \frac{N}{m} \right)\]or\[\frac{F}{l}=\frac{2{{i}_{1}}{{i}_{2}}}{a}\left( \frac{dyne}{cm} \right)\]
Direction of force : If conductors carries current in same direction, then force between them will be attractive. If conductor carries current in opposite direction, then force between them will be repulsive.
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