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Question

(A) The force per unit length between two parallel current-carrying conductors is given by the formula: $\frac{F}{l} = \frac{\mu_0 i_1 i_2}{2 \pi d}$.

Vedclass · Accepted Answer

$100$

Vedclass · Answer

(A) The force per unit length between two parallel current-carrying conductors is given by the formula: $\frac{F}{l} = \frac{\mu_0 i_1 i_2}{2 \pi d}$.Given: $l = 50 \ m$, $d = 0.2 \ m$, $F = 1 \ N$, and $\mu_0 = 4 \pi 	imes 10^{-7} \ T \cdot m/A$.Let the current in the second conductor be $i$. Then the current in the first conductor is $i_1 = 2i$.Substituting the values into the formula:$\frac{1}{50} = \frac{4 \pi 	imes 10^{-7} 	imes (2i) 	imes i}{2 \pi 	imes 0.2}$$\frac{1}{50} = 2 	imes 10^{-7} 	imes \frac{2i^2}{0.2}$$0.02 = 2 	imes 10^{-6} 	imes i^2$$i^2 = \frac{0.02}{2 	imes 10^{-6}} = 0.01 	imes 10^6 = 10^4$$i = \sqrt{10^4} = 100 \ A$.Therefore, the current in the second conductor is $100 \ A$.

Two parallel conductors, each $50 \ m$ long, separated by $0.2 \ m$, experience a force of $1 \ N$. If the current in the first conductor is twice that of the second conductor, what is the current in the second conductor (in $A$)? (Given: $\mu_0 = 4 \pi \times 10^{-7} \ T \cdot m/A$)

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