Question

at which angle must a charged particle be moving to experience the greatest magnetic force?
a. 90° to the magnetic field
b. 180° to the magnetic field
c. 45° to the magnetic field
d. 145° to the magnetic field

Explanation:

Step1: Recall the formula for magnetic force

The magnetic force on a charged particle is given by \(F = qvB\sin\theta\), 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.

Step2: Analyze the sine function

The sine function \(\sin\theta\) has a maximum value of \(1\). This occurs when \(\theta = 90^{\circ}\) since \(\sin(90^{\circ})=1\). For \(\theta = 180^{\circ}\), \(\sin(180^{\circ}) = 0\); for \(\theta=45^{\circ}\), \(\sin(45^{\circ})=\frac{\sqrt{2}}{2}\approx0.707\); for \(\theta = 145^{\circ}\), \(\sin(145^{\circ})=\sin(180 - 35)^{\circ}=\sin(35^{\circ})\approx0.574\).

Answer:

A. \(90^{\circ}\) to the magnetic field