A) \[\frac{{{\mu }_{2}}{{i}^{2}}}{{{b}^{2}}}\]
B) \[\frac{{{\mu }_{0}}{{i}^{2}}}{2\pi b}\]
C) \[\frac{{{\mu }_{0}}i}{2\pi {{b}^{2}}}\]
D) \[\frac{{{\mu }_{0}}i}{2\pi b}\]
Correct Answer: B
Solution :
Magnetic induction due to long wire at a distance b is \[B=\frac{{{\mu }_{0}}{{i}_{1}}}{2\pi b}\] and the force experienced by a conductor per unit length will be \[F=B{{i}_{2}}\] \[=\frac{{{\mu }_{0}}{{i}_{1}}{{i}_{2}}}{2\pi b}\] \[=\frac{{{\mu }_{0}}{{i}^{2}}}{2\pi b}\] \[[\because \,{{i}_{1}}={{i}_{2}}=i]\]
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