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(D) The force per unit length $f$ between two long parallel wires carrying currents $i_1$ and $i_2$ separated by a distance $r$ is given by the formul

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$10$

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(D) The force per unit length $f$ between two long parallel wires carrying currents $i_1$ and $i_2$ separated by a distance $r$ is given by the formula: $f = \frac{\mu_0 i_1 i_2}{2 \pi r}$ Given: $f = 4 	imes 10^{-5} \ N \ m^{-1}$ $r = 2.50 \ cm = 2.50 	imes 10^{-2} \ m$ $i_1 = 0.5 \ A$ $\mu_0 = 4 \pi 	imes 10^{-7} \ T \ m \ A^{-1}$ Substituting the values into the formula: $4 	imes 10^{-5} = \frac{4 \pi 	imes 10^{-7} 	imes 0.5 	imes i_2}{2 \pi 	imes 2.50 	imes 10^{-2}}$ $4 	imes 10^{-5} = \frac{2 	imes 10^{-7} 	imes 0.5 	imes i_2}{2.50 	imes 10^{-2}}$ $4 	imes 10^{-5} = \frac{10^{-7} 	imes i_2}{2.50 	imes 10^{-2}}$ $i_2 = \frac{4 	imes 10^{-5} 	imes 2.50 	imes 10^{-2}}{10^{-7}}$ $i_2 = 4 	imes 2.50 = 10 \ A$ Since the wires repel each other, the currents must be flowing in opposite directions.

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