Question

Three long, straight and parallel wires carrying currents are arranged as shown in figure. The force experienced by 10 cm length of wire Q is

• A. .4×10^–4 N towards the right
• B. 1.4×10^–4 N towards the left
• C. 2.6 × 10^–4 N to the right
• D. 2.6×10^–4 N to the left

Answer 1

Answer: (A)

.4×10^–4 N towards the right

Answer 2

Force on wire Q due to R;

$F _ { R } = 10 ^ { - 7 } \times \frac { 2 \times 20 \times 10 } { \left( 2 \times 10 ^ { - 2 } \right) } \times \left( 10 \times 10 ^ { - 2 } \right)$ = 2 × 10^–4 m

(Repulsive)

Force on wire Q due to P ;

$F _ { P } = 10 ^ { - 7 } \times 2 \times \frac { 10 \times 30 } { \left( 10 \times 10 ^ { - 2 } \right) } \times \left( 10 \times 10 ^ { - 2 } \right)$ = 0.6 × 10^–4 N

(Repulsive)

Hence net force F_net = F_R – F_P = 2 × 10^–4 – 0.6 × 10^–4 = 1.4 × 10^–4 N (towards right i.e. in the direction of $\overrightarrow { F _ { R } }$.