Concept:The magnetic force acting on a moving charged particle relies on the angle between its velocity vector and the magnetic field vector.
Formula:$$ F = qvB \sin(\theta) $$
Solution:- The term "perpendicular" indicates that the angle \( \theta \) between the electron's velocity and the magnetic field is exactly \( 90^\circ \).
- The sine function reaches its maximum possible value at this angle: \( \sin(90^\circ) = 1 \).
- Substitute this into the formula: \( F = qvB(1) = qvB \).
- Because the trigonometric multiplier is at its absolute peak, the resulting magnetic force acting on the electron is maximum.
Why other options are incorrect:Option B would only be true if the electron was moving parallel to the field (\( \theta = 0^\circ \)). Options A and C falsely equate the total force to just one of its component variables, ignoring velocity and the other parameters.
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