If a charged particle is thrown with double the speed in a region of transverse magnetic field, how do its radius and time period of revolution change?

Explanation

To solve the problem, we need to analyze how the radius of the circular path and the time period of revolution of a charged particle change when its speed is doubled in a transverse magnetic field.

### Step-by-Step Solution:

1. **Understanding the Motion of a Charged Particle in a Magnetic Field:**
When a charged particle moves in a magnetic field, it experiences a magnetic force that acts as a centripetal force, causing it to move in a circular path. The radius \( r \) of this circular path is given by the formula:
\[
r = \frac{mv}{qB}
...