An electron files into a homogeneous magnetic field of `10 ^(-3)` perpendicular to the force lines. The velocity of the electron is `v = 4 xx 10 ^(7)ms ^(-1)` what is the tangential acceleration of electron in the magnetic field ?

Options

A. `7xx10^(15)ms^(-2)`
B. `7xx10^(13)ms^(-2)`
C. `7xx10^(14)ms^(-2)`
D. zero

Answer

To find the tangential acceleration of an electron moving in a magnetic field, we can follow these steps:

### Step 1: Understand the motion of the electron in the magnetic field
When a charged particle (like an electron) moves in a magnetic field, it experiences a magnetic force given by the equation:
\[ F = q(\mathbf{v} \times \mathbf{B}) \]
where:
- \( F \) is the magnetic force,
- \( q \) is the charge of the particle,
- \( \mathbf{v} \) is the velocity vector of the particle,
- \( \mathbf{B} \) is the magnetic field vector.

### Step 2: Determine the direction of the force
Since the velocity of the electron is perpendicular to the magnetic field, the force will act perpendicular to both the velocity and the magnetic field. This means the force will cause the electron to move in a circular path rather than accelerating in the direction of the velocity.

### Step 3: Analyze the components of acceleration
In circular motion, there are two types of acceleration:
1. **Tangential acceleration** (\( a_t \)): This is due to a change in the speed of the particle along the circular path.
2. **Radial (centripetal) acceleration** (\( a_r \)): This is due to the change in direction of the velocity vector as the particle moves along the circular path.

### Step 4: Determine the tangential acceleration
In this case, since the magnetic force acts perpendicular to the velocity of the electron, it does not do any work on the electron. Therefore, the speed of the electron remains constant, and there is no tangential acceleration.

Mathematically, we can express this as:
\[ a_t = 0 \]
because there is no net force acting in the direction of the velocity.

### Conclusion
The tangential acceleration of the electron in the magnetic field is:
\[ a_t = 0 \, \text{m/s}^2 \]