Chapter 5.5, Problem 1aT

A small portion near the center of a large thin conducting plait is shown magnified at right. The portion shown has a net charge $Q_1$ and each side has an area $A_1$ .

Write an expression for the charge density on each side of the conducting plate.

To determine

The expression for charge density on each side of the conducting plate.

Explanation of Solution

Introduction:

The charge density is the ratio the charge distributed over a surface area. The expression for the charge density is given by,

  $\sigma =\frac{Q}{A}$

The distribution of the charge on the plate is shown below,

  

Figure 1

Now, because plate in uniform and charge on both the sides is same. So, the charge density on both the sides of the plate if the area of the sides is $A_{\text{l}}$ will also be same that is given by,

  $\begin{array}{c}{\sigma }_{\text{left}}={\sigma }_{\text{right}}\\ =\frac{\frac{1}{2}{Q}_{\text{l}}}{A_{\text{l}}}\end{array}$

Conclusion:

Therefore, the expression for the charge density on each side of the plate is $\frac{\frac{1}{2}{Q}_{\text{l}}}{A_{\text{l}}}$ .