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 being whirled in a horizontal circle, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Particle**:
- The charged particle experiences two primary forces:
- The tension (T) in the string, which provides the centripetal force necessary for circular motion.
- The magnetic force (F_m) due to the magnetic field when it is turned on.

2. **Centripetal Force Requirement**:
- For an object moving in a circle of radius \( r \) with speed \( v \), the required centripetal force is given by:
\[ F_c = \frac{mv^2}{r} \]
- Initially, when the magnetic field is off, the tension in the string provides this centripetal force:
\[ T = \frac{mv^2}{r} \]

3. **Introduce the Magnetic Field**:
- When the magnetic field \( B \) is turned on in the vertical direction, the charged particle experiences a magnetic force given by:
\[ F_m = q(v \times B) \]
- The direction of this force can be determined using the right-hand rule. Depending on the direction of the velocity \( v \) and the magnetic field \( B \), the magnetic force can either act towards the center of the circle or away from it.

4. **Analyze the Effect of the Magnetic Force**:
- If the magnetic force \( F_m \) acts towards the center of the circle (in the same direction as the centripetal force), the tension in the string will decrease:
\[ T' = \frac{mv^2}{r} - F_m \]
- If the magnetic force \( F_m \) acts away from the center (opposite to the centripetal force), the tension in the string will increase:
\[ T' = \frac{mv^2}{r} + F_m \]

5. **Conclusion**:
- The tension in the string can either increase or decrease depending on the direction of the magnetic force relative to the centripetal force. Thus, the tension in the string may increase or decrease when the magnetic field is applied.

### Final Answer:
The tension in the string may either increase or decrease depending on the direction of the magnetic force relative to the centripetal force.