An electron having charge `1.6xx10^(-19)C` and mass `9xx10^(-31)` kg is moving with `4xx10^(6)ms^(-1)` speed in a magnetic field `2xx10^(-1)` tesla in circular orbit. The force acting on electron and the radius of the circular orbit will be

Options

A. `12.8xx10^(-13)N,1.1xx10^(-4)m`
B. `1.28xx10^(-13)N,1.1xx10^(-3)m`
C. `1.28xx10^(-14)N,1.1xx10^(-4)m`
D. `1.28xx10^(-13)N,1.1xx10^(-4)m`

Answer

To solve the problem, we need to find the force acting on the electron and the radius of its circular orbit in a magnetic field. We will use the following formulas:

1. The magnetic force acting on a charged particle moving in a magnetic field is given by:
\[ F = q \cdot v \cdot B \]
where:
- \( F \) is the magnetic force,
- \( q \) is the charge of the particle,
- \( v \) is the velocity of the particle,
- \( B \) is the magnetic field strength.

2. The radius \( R \) of the circular orbit is given by:
\[ R = \frac{m \cdot v}{q \cdot B} \]
where:
- \( m \) is the mass of the particle.

### Step-by-Step Solution:

**Step 1: Identify the given values.**
- Charge of the electron, \( q = 1.6 \times 10^{-19} \, \text{C} \)
- Mass of the electron, \( m = 9.1 \times 10^{-31} \, \text{kg} \)
- Speed of the electron, \( v = 4 \times 10^{6} \, \text{m/s} \)
- Magnetic field strength, \( B = 2 \times 10^{-1} \, \text{T} \)

**Step 2: Calculate the force acting on the electron.**
Using the formula for magnetic force:
\[ F = q \cdot v \cdot B \]
Substituting the values:
\[ F = (1.6 \times 10^{-19} \, \text{C}) \cdot (4 \times 10^{6} \, \text{m/s}) \cdot (2 \times 10^{-1} \, \text{T}) \]

Calculating:
\[ F = 1.6 \times 4 \times 2 \times 10^{-19} \times 10^{6} \]
\[ F = 12.8 \times 10^{-13} \]
\[ F = 1.28 \times 10^{-12} \, \text{N} \]

**Step 3: Calculate the radius of the circular orbit.**
Using the formula for the radius:
\[ R = \frac{m \cdot v}{q \cdot B} \]
Substituting the values:
\[ R = \frac{(9.1 \times 10^{-31} \, \text{kg}) \cdot (4 \times 10^{6} \, \text{m/s})}{(1.6 \times 10^{-19} \, \text{C}) \cdot (2 \times 10^{-1} \, \text{T})} \]

Calculating:
\[ R = \frac{9.1 \times 4 \times 10^{-31} \times 10^{6}}{1.6 \times 2 \times 10^{-19}} \]
\[ R = \frac{36.4 \times 10^{-25}}{3.2 \times 10^{-20}} \]
\[ R = 1.14 \times 10^{-5} \, \text{m} \]

### Final Answers:
- The force acting on the electron is \( F = 1.28 \times 10^{-12} \, \text{N} \).
- The radius of the circular orbit is \( R = 1.14 \times 10^{-5} \, \text{m} \).