Question

Two long parallel wires carrying equal currents which are $8cm$ apart produce a magnetic field of $200\mu T$ mid way between them. The magnitude of the current in each wire is

• A. $10A$
• B. $20A$
• C. $300A$
• D. $40A$
• E. $50A$

Answer 1

The correct option is B $20A$

We know that magnetic field in parallel wires,
$B=\frac{{\mu }_0}{2\pi }\frac{i}{r}$
$\Rightarrow \frac{1}{2}\times 200\times {10}^{-6}=2\times {10}^{-7}\times \frac{i}{4\times {10}^{-2}}$
$\Rightarrow i=\frac{100\times {10}^{-6}\times 4\times {10}^{-2}}{2\times {10}^{-7}}$
$\Rightarrow i=\frac{100\times 4\times {10}^{-1}}{2}$
$\Rightarrow i=\frac{100\times 4}{2\times 10}$
$\Rightarrow i=20A$
Thus, current in each wire is $20A$.