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A beam of electrons is moving with constant velocity in a region having simultaneous perpendicular electric and magnetic fields of strength \( 20 \, \text{Vm}^{-1} \) and \( 0.5 \, \text{T} \) respectively at right angles to the direction of motion of the electrons. Then the velocity of electrons must be

1. 8 m/s
2. 20 m/s
3. 40 m/s
4. \( \frac{1}{40} \, \text{m/s} \)

Correct answer: 40 m/s

Solution

For the electrons to move with constant velocity, the electric force and magnetic force must balance each other. The condition is given by: \( qE = qvB \), where \( v \) is the velocity. Solving for \( v \), we get \( v = \frac{E}{B} = \frac{20}{0.5} = 40 \, \text{m/s} \).

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