A `3D` structure of current carrying wire is as shown in the figure.

The magnetic force experienced by a charge particle of mass `m` and charge `q`, when it is crossing origin with velocity `vec(v)` along positive `Y`-axis will be

Options

A. `((mu_(0)Iqv)/(8R)+(mu_(0)Iqv)/(4piR)) hati`
B. `(mu_(0)Iqv)/(8R)[(1+2/(pi))hati-hatk]`
C. `-(mu_(0)Iqv)/8 hatk`
D. zero

Answer

B

Explanation

The magnetic field at `O` is
`vec(B)=(mu_(0)I)/(4piR) hatk+(mu_(0)I)/(8R) hatk+(mu_(0)I)/(8R) hati`
`=(mu_(0)I)/(8R)[hati(1/2/(pi))hatk]`
`vec(F)=q(vec(v)xxvec(B))`
`=q[vhatjxx{(mu_(0)I)/(8R)[hati+(1+2/(pi))hatk]}hatk]`
`=(q_(0)Iqv)/(8R)[-hatk+(1+2/(pi)) hati]`