Question

A light beam traveling in the X-direction is described by \( E_y = 300 \sin(\omega (t - \frac{x}{c})) \, \text{volt/m}. \) An electron is constrained to move along the Y-direction with speed \( 0 \times 10^7 \, \text{m/s} \). Find the maximum magnetic force acting on the electron.

Hint:

The magnetic force on an electron moving in an electric field depends on its speed, the strength of the electric field, and the speed of light.

Answer 1

Step 1: Magnetic Force on Electron.
The magnetic force on the electron is given by: \[ F = e v B \] Where:
- \( e = 1.6 \times 10^{-19} \, \text{C} \) is the charge of the electron,
- \( v = 0 \times 10^7 \, \text{m/s} \) is the speed of the electron,
- \( B = \frac{E}{c} \) is the magnetic field, where \( E \) is the electric field.
Step 2: Maximum Magnetic Force.
The maximum magnetic force occurs when the electric field is at its peak: \[ F = e v \times \frac{E}{c} \] Substitute the values: \[ F = 1.6 \times 10^{-19} \times 0 \times 10^7 \times \frac{300}{3 \times 10^8} = 3.2 \times 10^{-15} \, \text{N} \]
Final Answer:
The maximum magnetic force acting on the electron is \( \boxed{3.2 \times 10^{-15} \, \text{N}} \).