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) = b hat(i) + c hat(k)`
B. `vec(E) = b hat(i) , vec(B) = c hat(k) + a hat(i)`
C. `vec(E) = 0, vec(B) = c hat(j) + b hat(k)`
D. `vec(E) = a hat(i) , vec(B) = c hat(k) + b hat(j)`

Answer

B

Explanation

Since electric field is either zero or along `+x`-axis, it can not deviate the path of the charged particle. In the options (1) and (3), path will be helical.
Since particle is deviate along `-y`-axis, hence magnetic force should be along `-y` direction.
Option (2) , `vec(F)_(m) = q[v hat(i) xx (c hat(k) + a hat(i))] = q[vchat(j) + 0]`
`= -qvc hat(j)`
Option (4) `vec(F)_(m) = q[v hat(i) xx (c hat(k) + b hat(i))] = q[-vc hat(j) + vb hat(k)]`
Since motion in `x-y` plane, option (4) is not correct
Option (2) is correct.