Question

A long straight cable contains $7$ strands of wire each carrying a current of $5A$. The magnetic induction at a distance of $2cm$ from the axis of the cable is

• A. $5\times {10}^{-5}T$
• B. $3.5\times {10}^{-6}T$
• C. $3.5\times {10}^{-4}T$
• D. $1.1\times {10}^{-3}T$

Answer 1

The correct option is C $3.5\times {10}^{-4}T$

$B=\frac{{\mu }_0{i}_{enclosed}}{2\pi r}$
$=\frac{4\pi \times {10}^{-7}\times 35}{2\times \pi \times 2\times {10}^{-2}}$ (each wire carries a current of $5A$ and there are $7$ wires so total current is $7\times 5A=35A$)
$=35\times {10}^{-5}T=3.5\times {10}^{-4}$