Magnetics 3 Question 6
6. Two thin long parallel wires separated by a distance $b$ are carrying a current $i$ ampere each. The magnitude of the force per unit length exerted by one wire on the other is $(1986,2 M)$
(a) $\frac{\mu _0 i^{2}}{b^{2}}$
(b) $\frac{\mu _0 i^{2}}{2 \pi b}$
(c) $\frac{\mu _0 i}{2 \pi b}$
(d) $\frac{\mu _0 i}{2 \pi b^{2}}$
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Answer:
Correct Answer: 6. (b)
Solution:
- Force per unit length between two wires carrying currents $i _1$ and $i _2$ at distance $r$ is given by
$$ \left.\right| _{\frac{F}{l}=\frac{\mu _0}{2 \pi} \frac{i _1 i _2}{r}} ^{\longleftarrow} $$
$$ \begin{array}{rlrl} \text { Here, } & & i _1 & =i _2=i \\ \text { and } & r & =b \\ & \therefore & \frac{F}{l} & =\frac{\mu _0 i^{2}}{2 \pi b} \end{array} $$
