A beam of electrons passes undeflected through uniformly perpendicular electric and magnetic fields. If the electric field is switched off, and the same magnetic field is maintained then the electrons move:

Options

A. in an elliptical orbit
B. in acircular orbit
C. along aparobolic path
D. along a straight line

Answer

To solve the problem, we need to analyze the motion of electrons in the presence of electric and magnetic fields, and how their motion changes when the electric field is switched off.

### Step-by-Step Solution:

1. **Understanding the Initial Condition**:
- A beam of electrons is moving through perpendicular electric (E) and magnetic (B) fields. The forces acting on the electrons are balanced, resulting in no deflection.
- The electric force (F_E) acting on the electrons is given by \( F_E = qE \) (where \( q \) is the charge of the electron).
- The magnetic force (F_B) acting on the electrons is given by \( F_B = qvB \) (where \( v \) is the velocity of the electrons).

2. **Condition for No Deflection**:
- For the electrons to pass undeflected, the electric force must equal the magnetic force:
\[ qE = qvB \]
- This simplifies to:
\[ E = vB \]
- This means the electric field strength (E) is equal to the product of the velocity of the electrons (v) and the magnetic field strength (B).

3. **Switching Off the Electric Field**:
- When the electric field is switched off, only the magnetic field remains. The electrons are now only influenced by the magnetic force.

4. **Effect of the Magnetic Field on Electrons**:
- The magnetic force acts perpendicular to the velocity of the electrons. According to the right-hand rule (or left-hand rule for negative charges), this force will cause the electrons to move in a circular path.
- The direction of the magnetic force on the electrons will cause them to experience centripetal acceleration, leading to circular motion.

5. **Conclusion**:
- Since the electric field is switched off and the magnetic field is maintained, the electrons will move in a circular orbit due to the magnetic force acting on them.

### Final Answer:
The electrons will move in a circular orbit.