For a positively charged particle moving in a `x-y` plane initially along the `x-axis` , there is a sudden change in its path due to the presence of electric and//or magnetic fields beyond `p` . The curved path is shown in the ` x- y `plane and is found to be non - circular. Which one of the following combinations is possible ?

Options

A. `vec(E)=0,vec(B)=bhat(i)+chat(k)`
B. `vec(E)=ahat(i),vec(B)=chat(k)+ahat(i)`
C. `vec(E)=0,vec(B)=chat(j)+bhat(k)`
D. `vec(E)=ahat(i),vec(B)=chat(k)+bhat(j)`

Answer

B

Explanation

`(b)` The velocity at `P` is in the `X-` direction ( given ). Let `vec(V)-mhat(i)` . After P, the positively charged particle gets deflected in the `x-y` plane toward `-y` direction and the path is non`-` circular. Now,
`vec(F)=q(vec(V)xxvec(B))=q[mhat(i)xx(chat(k)+ahat(i))]` for option
`(b)`
`=q[mchat(i)xxk+mahat(k)xxhat(i)]=mcq(-hat(j))`
Since in option `(b)`, electric field is also present `vec(E)=ahat(i)`, therefore it will also expert a force in the `+X` direction. The net result io of the two forces will be a non`-` circular path. Only option `(b)` fits fir the above logic. For other option, we get some other results.