An element `dvecl=dxhati` (where `dx=1cm`) is placed at the origin and carries a large current `i=10A`. What is the magnetic field on the Y-axis at a distance of `0.5m`?

Options

A. `2 xx 10^(-8)hat(k)T`
B. `4 xx 10^(-8)hat(k)T`
C. `-2 xx 10^(-8)hat(k)T`
D. `-4 xx 10^(-8)hat(k)T`

Answer

B

Explanation

Here, dl=dx=1cm=`10^(-2)m`, i=10A, r=0.5 m
`therefore` `dB=(mu_(0)/(4pi).(i(dlxxr)/r^(3))`
`=(mu_(0)/(4pi).(idl)/r^(2)(hat(i) xx hat(j)) = (mu_(0))/(4pi).(idl)/r^(2)hat(k)`
`=(10^(-7) xx 10 xx 10^(-2)sin90^(@))/(0.5)^(2)hat(k)`
`=4 xx 10^(-8)hat(k)T`