Answer to Question #170946 in Electric Circuits for Miriam Vogel

Question

A point charge of 5 µC is located at point A between two plates 40 cm apart. The potential of the upper plate is 1000 V and the lower plate is at zero. The geometry of the situation is shown in Figure 7.4. Calculate the force on the charge when it is at A.

Answer 1

Explanations & Calculations

• Refer to the sketch attached

• What is to be known in these types of questions is that, there exist an electromagnetic field in between the plates which is given by $\vec{E}=\Large \frac{\Delta V}{d}\small\cdots(1)$, where $\small \Delta V$ is the potential difference in the region between the plates & d, the separation between the plates.

• And when there is a charge placed in an electric field, an electromagnetic force is generated on that which is given by $\small \vec{F}=\vec{E}q$: along the same direction as the field if the charge is a positive one & in the reversed direction if the charge is negative.

• And it can be seen by the above equation (1) that the field does not change with the position between the plates: it is constant throughout between them.
• Therefore, a constant force is generated on the charge no matter the position it is placed.

• Then,

$\qquad\qquad \begin{aligned} \small \vec{F}&=\small \vec{E}q\\ &=\small \Big[\frac{(1000-0)V}{0.40m}\Big]\times (5\times 10^{-6}C )\\ &=\small \bold{0.0125\,N} \end{aligned}$