Magnetic force

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Question

Consider three long straight parallel wires as shown in figure. The force experienced by a 25 cm length of wire C is n $\times$ 10^-4N. Find the value of n?

Moderate

Solution

$R e p u l s i o n b y w i r e D, F_{1} = \frac{μ_{0}}{2 π} \frac{i_{1} i_{2} l}{r} [t o w a r d s r i g h t] = \frac{(2 \times 10^{- 7}) (30 \times 10)}{3 \times 10^{- 2}} (0.25) = 5 \times 10^{- 4} N Repulsion by wire G, = F_{2} = \frac{(2 \times 10^{- 7}) (20 \times 10)}{5 \times 10^{- 2}} (0.25) = 2 \times 10^{- 4} N ∴ F_{net} = F_{1} - F_{2} = 3 \times 10^{- 4} N$

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