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

 

Electric field can deviate the path of the particle in the shown direction only when it is along negative y-direction. In the given options   is either zero or along x-direction. Hence it is the magnetic field which is really responsible for its curved path. Options (a) and (c) can’t be accepted as the path will be helix in that case (when the velocity vector makes an angle other than 0°, 180° or 90° with the magnetic field, path is a helix) option (d) is wrong because in that case component of net force on the particle also comes in k direction which is not acceptable as the particle is moving in x-y plane. Only in option (b) the particle can move in x-y plane.

In option (d) :${\overrightarrow{\mathrm{F}}}_{\mathrm{net}}=\mathrm{q}\overrightarrow{\mathrm{E}}+\mathrm{q}(\overrightarrow{\mathrm{v}}\times \overrightarrow{\mathrm{B}})$

Initial velocity is along x-direction. So let $\overrightarrow{\mathrm{v}}=\mathrm{v}\hat{\mathrm{i}}$

$\therefore {\overrightarrow{\mathrm{F}}}_{\mathrm{net}}=\mathrm{qa}\hat{\mathrm{i}}+\mathrm{q}\left[\right(\mathrm{v}\hat{\mathrm{i}})\times (\mathrm{c}\hat{\mathrm{k}}+\mathrm{b}\hat{\mathrm{j}}]=\mathrm{qa}\hat{\mathrm{i}}-\mathrm{qvc}\hat{\mathrm{j}}+\mathrm{qvb}\hat{\mathrm{k}}$

The charge will go out of the plane in this case. 

In option (b)  ${\overrightarrow{\mathrm{F}}}_{\text{net }}=\mathrm{q}\left(\mathrm{a}\hat{\mathrm{i}}\right)+\mathrm{q}\left[\right(\mathrm{v}\hat{\mathrm{i}})\times (\mathrm{c}\hat{\mathrm{k}}+\mathrm{a}\hat{\mathrm{i}})=\mathrm{qa}\hat{\mathrm{i}}-\mathrm{qvc}\hat{\mathrm{j}}$

The charge will be in xy plane but will have a non circular trajectory.