Question

An electron falling freely under the influence of gravity enters a uniform magnetic field directed towards south. The electron is initially deflected towards?

• A. east
• B. west
• C. north
• D. south

Hint:

To determine the direction of force on a moving charge in a magnetic field, use the right-hand rule for positive charges and reverse it for electrons. The force is always perpendicular to both the velocity and the magnetic field.

Answer 1

The Correct Option is A

Step 1: Understanding the motion of the electron 
- The electron is initially moving downward due to gravity. - It enters a uniform magnetic field directed towards the south. - The force on a charged particle moving in a magnetic field is given by the Lorentz force: \[ \mathbf{F} = q (\mathbf{v} \times \mathbf{B}) \] where: - \( q \) is the charge of the electron (\( -e \)), - \( \mathbf{v} \) is the velocity vector of the electron, - \( \mathbf{B} \) is the magnetic field vector. 

Step 2: Apply the Right-Hand Rule (Fleming's Left-Hand Rule) 
- The velocity \( \mathbf{v} \) of the electron is downward (\( -\hat{z} \)). - The magnetic field \( \mathbf{B} \) is directed towards the south (\( -\hat{y} \)). - Using the cross-product \( \mathbf{v} \times \mathbf{B} \): \[ (-\hat{z}) \times (-\hat{y}) = \hat{x} \text{ (towards east)} \] Since the electron has a negative charge, the force acts in the opposite direction to the computed cross-product, meaning the electron is deflected towards the east.