Question

1. which one of the following statements concerning the magnetic for a charged particle in a magnetic field is true? a) the magnetic force is a maximum if the particle is stationary. b) the magnetic force is zero if the particle moves perpendicular to the field. c) the magnetic force is a maximum if the particle moves parallel to the field. d) the magnetic force acts in the direction of motion for a positively charged particle. e) the magnetic force depends on the component of the particles velocity that is perpendicular to the field.

Explanation:

The formula for the magnetic force on a charged particle is \(F = qvB\sin\theta\), where \(q\) is the charge, \(v\) is the velocity, \(B\) is the magnetic field, and \(\theta\) is the angle between the velocity and the magnetic field.

• For option A: If the particle is stationary (\(v = 0\)), then \(F=0\), so A is false.
• For option B: If \(\theta = 90^{\circ}\) (perpendicular), \(F = qvB\) (maximum), so B is false.
• For option C: If \(\theta = 0^{\circ}\) (parallel), \(F = 0\), so C is false.
• For option D: The magnetic force is perpendicular to the direction of motion (using the right - hand rule), so D is false.
• For option E: Since \(F = qvB\sin\theta\), and \(\sin\theta\) is related to the perpendicular component of velocity (\(v_{\perp}=v\sin\theta\)), the force depends on the perpendicular component of velocity.

Answer:

E. The magnetic force depends on the component of the particle's velocity that is perpendicular to the field.