Magnetic force

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Question

Consider three long straight parallel wires as shown in figure. Find the force experienced by a 25 cm length of wire C ( $μ$ N)

Moderate

Solution

Repulsion by wire D, $F_{1} = \frac{μ_{0}}{2 π} \frac{i_{1} i_{2} l}{r}$ towards right]
$= \frac{(2 \times 10^{- 7}) (30 \times 10)}{3 \times 10^{- 2}} (0 .25) = 5 \times 10^{- 4} N$
Repulsion by wire G,
$\begin{array}{l} F_{2} = \frac{(2 \times 10^{- 7}) (20 \times 10)}{5 \times 10^{- 2}} (0 .25) = 2 \times 10^{- 4} N \\ ∴ F_{net} = F_{1} - F_{2} = 300 \times 10^{- 6} N \end{array}$

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