A wire lying along y-axis from `y=0` to `y=1 m` carries a current of `2mA` in the negative y-direction. The wire lies in a non uniform magnetic field given by `B=(0.3T/m)yhati +(0.4Tm)yhatj`. The magnetic force on the entire wire is

Options

A. `-3xx10^-4hatjN`
B. `6xx10^-3hatkN`
C. `-3xx10^-4hatkN`
D. `3xx10^-4hatkN`

Answer

D

Explanation

Due to hatj component of `B` magnetic force is zero. It is only due to hati component.
`I` is towards-y direction B is towards hati direction.
Hence `IxxB` (the direction of magnetic force is `+hatk)`
`F=intdF=int_0^1(i)(dy)(B)`
`=int_0^1(2xx10^-3)(dy)(0.3y)`
`=3xx10^-4N`