Question

The magnetic induction due to a straight current-carrying conductor of infinite length at a distance d from it will be

• A. $\frac{{\mu }_{0}i}{2d}$
• B. $\frac{{\mu }_{0}i}{2\pi d}$
• C. zero
• D. $\frac{{\mu }_{0}i}{4\pi d}$

Answer 1

Answer: (B)

$\frac{{\mu }_{0}i}{2\pi d}$

The magnetic induction due to a straight current-carrying conductor of infinite length at a distance d from it will be obtain by considering circule element dl around it,
$\oint B.dl={\mu }_{0}i$
$B\oint dl={\mu }_{0}i$
$B2\pi d={\mu }_{0}i$.....(since circumference of circle is $2\pi d$)
$B=\frac{{\mu }_{0}i}{2\pi d}$