First slide

Force on a current carrying wire placed in a magnetic field

Question

Three long, straight parallel wires carrying current, are arranged as shown in figure. The force experienced by a 25 cm length of wire C is

Moderate

A

$10^{- 3} N$
B

$2.5 \times 10^{- 3} N$
C

Zero
D

$1.5 \times 10^{- 3} N$

Solution

Force on wire C due to wire D,
$F_{D} = 10^{- 7} \times \frac{2 \times 30 \times 10}{3 \times 10^{- 2}} \times 25 \times 10^{- 2} = 5 \times 10^{- 4} N$
(Towards right)
Force on wire C due to wire G,
$\begin{array}{l} F_{G} = 10^{- 7} \times \frac{2 \times 20 \times 10}{2 \times 10^{- 2}} \times 25 \times 10^{- 2} = 5 \times 10^{- 4} N \\ \Rightarrow Net force on wire C is F_{net} = F_{D} - F_{G} = 0 \end{array}$ (Towards left)

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