A, B and C are parallel conductors of equal l | vedclass

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Question

(B) The force per unit length between two parallel conductors carrying currents $i_1$ and $i_2$ separated by distance $r$ is given by $f = \frac{\mu_0

Vedclass · Accepted Answer

$F_2 = 2F_1$

Vedclass · Answer

(B) The force per unit length between two parallel conductors carrying currents $i_1$ and $i_2$ separated by distance $r$ is given by $f = \frac{\mu_0}{2\pi} \frac{i_1 i_2}{r}$.For conductor $A$ and $B$: Both carry current $I$ in the same direction,so the force $F_1$ exerted by $B$ on $A$ is attractive.$F_1 = \frac{\mu_0}{2\pi} \frac{I \cdot I}{x} = \frac{\mu_0 I^2}{2\pi x}$.For conductor $B$ and $C$: $B$ carries current $I$ and $C$ carries current $2I$ in opposite directions,so the force $F_2$ exerted by $C$ on $B$ is repulsive.$F_2 = \frac{\mu_0}{2\pi} \frac{I \cdot 2I}{x} = \frac{2 \mu_0 I^2}{2\pi x} = 2 F_1$.Since $F_1$ is attractive and $F_2$ is repulsive,they act in opposite directions. Thus,$F_2 = -2F_1$ or $F_1 = -0.5 F_2$. However,looking at the magnitudes and directions,the force $F_2$ is twice the magnitude of $F_1$ and acts in the opposite direction. Given the options,$F_2 = 2F_1$ represents the relationship between the magnitudes.

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