A uniform magnetic field at right angles to the direction of motion of electron . As a result , the electron moves in circular parth of radius 2 cm . If the speed of electron is doubles , then the radius of the circular path will be

Options

A. 2.0 cm
B. 0.5 cm
C. 4.0 cm
D. 1.0 cm

Explanation

To solve the problem, we need to understand the relationship between the radius of the circular path of an electron moving in a magnetic field and its speed.

### Step-by-Step Solution:

1. **Understand the relationship**: The radius \( R \) of the circular path of a charged particle (like an electron) moving in a magnetic field is given by the formula:
\[ R = \frac{mv}{qB} \]
where:
- \( m \) is the mass of the electron,
- \( v \) is the speed of the electron,
- \( q \) is the charge of the electron,
- \( B \) is the magnetic field strength.

2. **Initial conditions**: We know that initially, the radius \( R \) is 2 cm when the speed of the electron is \( v \).

3. **Doubling the speed**: If the speed of the electron is doubled, then the new speed \( v' \) is:
\[ v' = 2v \]

4. **Calculate the new radius**: Substituting \( v' \) into the radius formula gives:
\[ R' = \frac{m(2v)}{qB} = 2 \cdot \frac{mv}{qB} = 2R \]
Since the initial radius \( R \) is 2 cm, the new radius \( R' \) will be:
\[ R' = 2 \times 2 \text{ cm} = 4 \text{ cm} \]

5. **Conclusion**: Therefore, if the speed of the electron is doubled, the radius of the circular path will be 4 cm.

### Final Answer:
The radius of the circular path will be **4 cm**.

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