At `t=0` a charge q is at the origin and moving in the y-direction with velocity `vec(v)=vhat(j)`. The charge moves in a magnetic field that is for `ygt0` out of page and given by `B_(1)hat(z)` and for `ylt0` into the page and given `-B_(2)hat(z)`. The charge's subsequent trajectory is shown in the sketch. From this information, we can deduce that

Options

A. `qgt0"and"|B_(1)|lt|B_(2)|`
B. `qlt0"and"|B_(1)|lt|B_(2)|`
C. `qgt0"and"|B_(1)|gt|B_(2)|`
D. `qlt0"and"|B_(1)|gt|B_(2)|`

Answer

A

Explanation

`vec(F)=q(vec(V)xxvec(B))`
`B=B_(1)hat(k)`
`V=Vhat(j)`
Force at origin is along x axis.
`hat(j)xxhat(k)=hat(i) " ""so q should be positive"`.
`r=(mV)/(qB)`
`because r_(2)ltr_(1)`
`therefore |B_(2)|gt|B_(1)|`