A charged particle is whirled in a horizontal circle on a frictionless table by attaching it to a string fixed at one pint. If a magnetic field is switched on in the vertical direction, the tension in the string

Options

A. will increase
B. will decrease
C. will remai the same
D. may increase or decrease

Answer

To solve the problem of how the tension in the string changes when a magnetic field is applied to a charged particle moving in a horizontal circle, we can follow these steps:

### Step-by-Step Solution

1. **Understanding the Initial Conditions**:
- A charged particle with mass \( m \) and charge \( q \) is whirled in a horizontal circle with radius \( L \).
- The tension \( T \) in the string provides the necessary centripetal force to keep the particle in circular motion.

2. **Centripetal Force Before the Magnetic Field**:
- The centripetal force required for circular motion is given by:
\[ F_c = \frac{mv^2}{L} \]
- Here, \( v \) is the speed of the particle.

3. **Effect of the Magnetic Field**:
- When a magnetic field \( B \) is applied vertically (either upwards or downwards), it exerts a magnetic force on the charged particle.
- The magnetic force \( F_m \) acting on the particle is given by:
\[ F_m = q(v \times B) \]
- The direction of this force can be determined using the right-hand rule.

4. **Case 1: Magnetic Field in the Upward Direction**:
- If the magnetic field is directed upwards, the magnetic force will act outward (away from the center).
- The tension in the string must now counteract both the centripetal force and the magnetic force:
\[ T = F_c + F_m \]
- Thus, the tension increases when the magnetic field is switched on in this direction.

5. **Case 2: Magnetic Field in the Downward Direction**:
- If the magnetic field is directed downwards, the magnetic force will act inward (towards the center).
- In this case, the tension in the string will be reduced because the magnetic force assists in providing the necessary centripetal force:
\[ T = F_c - F_m \]
- Thus, the tension decreases when the magnetic field is switched on in this direction.

6. **Conclusion**:
- Depending on the direction of the magnetic field, the tension in the string can either increase or decrease. Therefore, the answer is that the tension may increase or may decrease.

### Final Answer:
The tension in the string may increase or may decrease depending on the direction of the magnetic field.