Question

The electric field is constant over each face of the cube shown in FIGURE EX24.4. Does the box contain positive charge, negative charge, or no charge? Explain.

Short answer

The box has a negative charge.

Step-by-step solution

Step 1. Given Information

Over each face of the cube illustrated, the electric field is constant.

Step 2. Is there a positive charge, a negative charge, or no charge in the box?

According to Gauss's law $\oint \overrightarrow{E}·\overrightarrow{dA}=\frac{Q}{{\epsilon }_0}$,

Here E is the electric field, A is the area, Q is the charge and ${\epsilon }_0$is a constant

Now apply Gauss's law, to get

$\begin{array}{rcl}\frac{Q}{{\epsilon }_0}& =& \oint \overrightarrow{E}·\overrightarrow{dA}\\ & =& (-15-20-15+20+15+10)\mathrm{A}\\ & =& -5\mathrm{A}\end{array}$

So, let have charge$Q=5A{\epsilon }_0<0$

$\Rightarrow$The box has negative charge

Gauss's law for electric flux is used to determine the charge of the box.