An electron is travelling along the \(x\) -direction. It encounters a magnetic field in the \(y\) -direction. Its subsequent motion will be

If a particle carrying charge \(q\) and moving with velocity \(v\) through a point in magnetic field experiences a deflecting force \(F\), then magnetic field \(\overrightarrow{\mathbf{B}}\) is given by

Here,
\(
\begin{array}{l}
\overrightarrow{\mathbf{F}}=q \overrightarrow{\mathbf{v}} \times \overrightarrow{\mathbf{B}} \\
\overrightarrow{\mathbf{v}}=v_{x} \hat{\mathbf{i}} \text { and }
\end{array}
\)
\(
\overrightarrow{\mathbf{B}}=B_{y} \hat{\mathbf{j}}
\)
\(\therefore\)
\(
\overrightarrow{\mathbf{F}}=e v_{x} B_{y}(\hat{\mathbf{i}} \times \hat{\mathbf{j}})=e v_{x} B_{y} \hat{\mathbf{k}}
\)
Hence, subsequent motion of the charged particle will be a circle in the \(x y\) -plane.