An electron enters a region where the magnetic field B and the electr…

The correct answer is Option (4) → it can also go undeflected

A charge moving in both fields feels the Lorentz force \( \vec{F}=q\,(\vec{E}+\vec{v}\times\vec{B}) \), the sum of an electric part and a magnetic part. For an electron, \( q=-e \).

Option (1) it will always move in the direction of \( \vec{B} \) — Incorrect. The magnetic force \( q\,\vec{v}\times\vec{B} \) is perpendicular to \( \vec{B} \), and the electric force is along \( \vec{E} \), which is also perpendicular to \( \vec{B} \). No force acts along \( \vec{B} \) to turn the electron that way.

Option (2) it will always move in the direction of \( \vec{E} \) — Incorrect. The electric force on an electron, \( -e\vec{E} \), is opposite to \( \vec{E} \). The magnetic force adds a sideways push. So the electron is not carried along \( \vec{E} \).

Option (3) it always moves in a circle — Incorrect. Uniform circular motion needs a force of constant size always perpendicular to the velocity, as in a magnetic field alone. The electric force does work on the electron and changes its speed, so the path is in general not a circle.

Option (4) it can also go undeflected — Correct. If the electron moves perpendicular to both fields with speed \( v=E/B \), the electric force \( eE \) and the magnetic force \( evB \) can be equal and opposite. The net force is then zero and the electron goes straight through undeflected.