An extremely long straight wire, with radius of cross-section a, carries current I. Then ratio of magnetic fields at distances `a/2` and 2a from its axis would be ______ .

Options

A. `1/4`
B. 4
C. `1/2`
D. 1

Answer

D

Explanation

For first point, `B_(i)=(mu_(0)I)/(2pia^(2))(r)`
`thereforeB_(i)=(mu_(0)I)/(2pia^(2))(a/2)=(mu_(0)I)/(4pia)" "...(1)`
For second point, `B_(0)=(mu_(0)I)/(2pia^(2))`
`thereforeB_(0)=(mu_(0)I)/(2pi(2a))=(mu_(0)I)/(4pia)" "...(2)`
From equation (1) and (2),
`B_(i)/B_(0)=1`