Question

Current i is flowing in a long straight conducting wire. The magnetic induction at a distance r from it is 0.4 Tesla, then its value at double the distance will be

• A. 1.6 Tesla
• B. 0.8 Tesla
• C. 0.2 Tesla
• D. 0.1 Tesla

Answer 1

The correct option is C 0.2 Tesla

The magnetic induction at a distance r from a long straight conducting wire carrying current i is given as

$B=\frac{{\mu }_{0}i}{2\pi r}$....(1)

Now, if the distance doubles,

$B^{\prime }=\frac{{\mu }_{0}i}{4\pi r}$

$B^{\prime }=\frac{1}{2}\frac{{\mu }_{0}i}{2\pi r}$

from (1),

$B^{\prime }=\frac{1}{2}B=\frac{1}{2}\left(0.4\right)=0.2T$