Two long straight wires, each carrying an electric current of 5 A,...

Two long straight wires, each carrying an electric current of 5 A, are kept parallel to each other at a separation of 2.5 cm. Find the magnitude of the magnetic force experiment by 10 cm of a wire.

Options

A $4.0 \times 10^{-4} \mathrm{~N}$
B $3.5 \times 10^{-6} \mathrm{~N}$
C $2.0 \times 10^{-5} \mathrm{~N}$
D $2.0 \times 10^{-9} \mathrm{~N}$

Correct answer

C. $2.0 \times 10^{-5} \mathrm{~N}$

Step-by-step solution

The field at the site of one wire due to the other is

\begin{aligned} B & =\frac{\mu_0 i}{2 \pi d}=\frac{2 \times 10^7 \times 5.0}{2.5 \times 10^{-2}} \\ & =4.0 \times 10^{-5} \mathrm{~T}\end{aligned}

The force experienced by 10 cm of this wire due to other is

\begin{aligned} F & =i l B \\ & =(5.0) \times\left(10 \times 10^{-2}\right) \times\left(4.0 \times 10^{-5}\right) \\ & =2 \times 10^{-5} \mathrm{~N}\end{aligned}

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