A charge q is moving with a velocity `v_(1)=1hati` m/s at a point in a magentic field and experiences a force `F=q[-hatj+1hatk]` N. If the charge is moving with a voloctiy `v_(2)=2hatj` m/s at the same point then it experiences a force `F_(2)=q(1hati-1hatk)` N. The magnetic induction B at that point is

Options

A. `(hatl+hatj+hatk)wb//m^(2)`
B. `(hatl-hatj+hatk)wb//m^(2)`
C. `(-hatl+hatj-hatk)wb//m^(2)`
D. `(hatl+hatj-hatk)wb//m^(2)`

Answer

A

Explanation

Let the magnetic field is,
`B=B_(1)hati+B_(2)hatj+B_(3)hatk`
Applying `F_(m)=q(vxxB)` two times, we have
`q[-hatj+hatk]=q[(hati)xxB_(1)hati+B_(2)hatj+B_(3)hatk)]=q[B_(2)hatk-B_(3)hatj]`
On comparing two sides, we get
`B_(2)=1andB_(3)=1`
Further, `q[hati-hatk]=q[(hatj)xxB_(1)hati+B_(3)hatk)]=q[-B_(1)hatk+B_(3)hati]`
Agnin comparing we get
`B_(1)=1andB_(3)=1`
`:.B=(hati+hatj+hatk)Wb//m^(2)`