Question

Two horizontal parallel plates are conducting in a vacuum.

A small particle of mass 4 × 10^-12kg, carrying a positive charge of 3.0 × 10^-14C is released at A close to the upper plate. What total force acts on this particle?

Answer 1

Explanation & Calculations

• Since the plates are conducting, they generate a magnetic field around them.
• Plates should be conducting in opposite directions in order to maintain an effective magnetic field between the plates otherwise they cancel out.
• Consider the figure attached

• $\small B = \frac{1}{2}\mu_0J$ : $\small j=$ current per unit length of the plate
• This field generates a force (F) on the charge as shown (according to the left-hand rule)

$\qquad\qquad \small F=2Bqv$

• As the particle is released from rest, F=0 at the beginning & increases as it falls down under gravity.
• Therefore, the net force which continues to act is

$\qquad\qquad \begin{aligned} \small F_{net}&= \small \sqrt{mg^2+F^2}\\ &= \small \sqrt{(mg)^2+(2Bqv)^2} \end{aligned}$

• This moves the particle in a trajectory.