If cathode rays are projected at right angles to a magnetic field, their trajectory is:

Options

A. Ellipse
B. Circle
C. Parabola
D. None of these

Answer

To solve the question about the trajectory of cathode rays projected at right angles to a magnetic field, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Cathode Rays**:
Cathode rays are streams of electrons, which are negatively charged particles.

2. **Magnetic Force on Charged Particles**:
When a charged particle moves in a magnetic field, it experiences a magnetic force given by the equation:
\[ F_m = q v B \sin \theta \]
where:
- \( F_m \) is the magnetic force,
- \( q \) is the charge of the particle,
- \( v \) is the velocity of the particle,
- \( B \) is the magnetic field strength,
- \( \theta \) is the angle between the velocity vector and the magnetic field vector.

3. **Setting the Angle**:
In this case, the cathode rays are projected at right angles to the magnetic field, meaning \( \theta = 90^\circ \). Therefore, \( \sin 90^\circ = 1 \), and the magnetic force simplifies to:
\[ F_m = q v B \]

4. **Direction of the Force**:
The magnetic force acts perpendicular to both the velocity of the cathode rays and the direction of the magnetic field. This can be represented using the vector cross product:
\[ \vec{F_m} = q \vec{v} \times \vec{B} \]

5. **Centripetal Force**:
Since the magnetic force is always perpendicular to the velocity of the cathode rays, it acts as a centripetal force, causing the rays to move in a circular path.

6. **Conclusion**:
As a result, the trajectory of the cathode rays when projected at right angles to the magnetic field will be circular.

### Final Answer:
The trajectory of cathode rays projected at right angles to a magnetic field is circular.

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