First slide

Force on a current carrying wire placed in a magnetic field

Question

Two long parallel wires carrying equal current separated by 1 m, exert a force of $2 \times 10^{- 7} N / m$ on one another. The current flowing through them is

Easy

A

2.0 A
B

$2 .0 \times 10^{- 7} A$
C

1.0 A
D

$1 .0 \times 10^{- 7} A$

Solution

$\begin{array}{l} \frac{F}{l} = \frac{μ_{0}}{4 π} \times \frac{2 i_{1} \times i_{2}}{a} = \frac{μ_{0}}{4 π} \frac{2 i^{2}}{a} (∵ i_{1} = i_{2} = i) \\ \Rightarrow 2 \times 10^{- 7} = 10^{- 7} \times \frac{2 i^{2}}{1} \Rightarrow i = 1 A \end{array}$

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