In a chamber, a uniform magnetic field of `6*5G(1G=10^-4T)` is maintained. An electron is shot into the field with a speed of `4*8xx10^6ms^-1` normal to the field. (i) Explain why the path of the electron is a circle. Determine the radius of the circular orbit. `(e=1*6xx10^(-19)C, m_e=9*1xx10^(-31)kg)`.

Explanation

To solve the problem step-by-step, we will first explain why the path of the electron is circular and then calculate the radius of the circular orbit.

### Step 1: Explain why the path of the electron is circular

When a charged particle, like an electron, moves through a magnetic field, it experiences a force known as the Lorentz force. This force is given by the equation:

\[ \mathbf{F} = q (\mathbf{v} \times \mathbf{B}) \]

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