Question

1. *distinguish between the type of motion a charged particle experiences as it moves through gravitational, electric, and magnetic fields.

Explanation:

• Gravitational field: A charged particle experiences a force \(F = mg\) (where \(m\) is mass and \(g\) is acceleration due to gravity). If the initial velocity is at an angle to the gravitational - field direction, the motion is projectile - like (parabolic if \(g\) is constant). If the initial velocity is parallel or anti - parallel to the gravitational field, the motion is one - dimensional (linear) with constant acceleration \(a = g\).
• Electric field: The force on a charged particle \(q\) is \(F=qE\) (where \(E\) is the electric field). If the initial velocity is at an angle to the electric - field direction, the motion is similar to projectile motion (parabolic if \(E\) is uniform). If the initial velocity is parallel or anti - parallel to the electric field, the motion is one - dimensional (linear) with constant acceleration \(a=\frac{qE}{m}\).
• Magnetic field: The force on a charged particle \(q\) moving with velocity \(v\) is \(F = qvB\sin\theta\) (where \(B\) is the magnetic field and \(\theta\) is the angle between \(v\) and \(B\)).
• If \(\theta = 0^{\circ}\) or \(\theta=180^{\circ}\) (\(v\parallel B\)), \(F = 0\), and the particle moves with constant velocity (uniform motion).
• If \(\theta = 90^{\circ}\) (\(v\perp B\)), the force acts as a centripetal force, and the particle moves in a circular path with radius \(r=\frac{mv}{qB}\).
• If \(0^{\circ}<\theta < 90^{\circ}\) or \(90^{\circ}<\theta < 180^{\circ}\), the motion is a helical path. The component of velocity parallel to \(B\) (\(v_{\parallel}=v\cos\theta\)) gives a linear motion along the \(B\) - direction, and the component of velocity perpendicular to \(B\) (\(v_{\perp}=v\sin\theta\)) gives a circular motion in the plane perpendicular to \(B\).

Answer:

• In a gravitational field, the motion is similar to projectile (if initial velocity is at an angle) or linear (if initial velocity is parallel/anti - parallel) with acceleration \(a = g\).
• In an electric field, the motion is similar to projectile (if initial velocity is at an angle to \(E\)) or linear (if initial velocity is parallel/anti - parallel to \(E\)) with acceleration \(a=\frac{qE}{m}\).
• In a magnetic field:
• If \(v\parallel B\), the motion is uniform (constant velocity).
• If \(v\perp B\), the motion is circular with radius \(r = \frac{mv}{qB}\).
• If \(v\) has both parallel and perpendicular components to \(B\), the motion is helical.