Question

The particles with the following speed pass undeflected in the region of crossed fields

• A. \( \mathbf{E} \cos \theta \)
• B. \( \frac{\mathbf{E}}{\mathbf{B}} \)
• C. \( \frac{\mathbf{E}}{\mathbf{B}^2} \)
• D. \( \frac{\mathbf{E}^2}{\mathbf{B}} \)

Hint:

In crossed electric and magnetic fields, the particle will remain undeflected if its speed equals the ratio of electric field strength to magnetic field strength.

Answer 1

The Correct Option is B

When a charged particle moves through crossed electric and magnetic fields, the particle moves undeflected when the electric force and magnetic force balance each other. The electric force is \( qE \) and the magnetic force is \( qvB \), where \( v \) is the speed of the particle. For no deflection, we have: \[ qE = qvB \quad \Rightarrow \quad v = \frac{E}{B} \]
Thus, the speed of the particle is \( \frac{E}{B} \).