An alpha particle moving with a velocity `vec(v)_(1)=2hat(i)m//s` is a uniform magnetic field experiences a force `vec(F)_(1)=-4e(hat(j)-hat(k))N`. When the particle moves with a velocity `vec(v)_(2)=hat(j)m//s`, then the force experienced by it is `vec(F)_(2)=2e(hat(i)-hat(k))N`. The magnetic induction `vec(B)` at that point is `:`

Options

A. `hat(i)+hat(j)-hat(k)`
B. `-hat(i)-hat(j)+hat(k)`
C. `hat(i)-hat(j)-hat(k)`
D. `hat(i)+hat(j)+hat(k)`

Answer

D

Explanation

`vec(B)=xhat(i)+yhat(j)+zhat(k)`
`vec(F_(1))=2[2hat(i)xx(xhat(i)+yhat(j)+zhat(k))]=-4e(hat(j)-hat(k))`
`vec(F_(2))=2e[2hat(j)xx(xhat(i)+yhat(j)+zhat(k))]=2e(hat(i)-hat(k))`
`impliesvec(B)=hat(i)+hat(J)+hat(k)`