Question

You find a sealed box on your doorstep. You suspect that the box contains several charged metal spheres packed in insulating material. How can you determine the total net charge inside the box without opening the box? Or isn’t this possible?

Short answer

It is possible to determine the net charge inside by box, by first calculating the electric field by a test charge and then calculating the electric flux by using Gauss’s law.

Step-by-step solution

How to determine electric charge

To determine the net electric charge inside the box without opening it. We can use a test charge to determine if there is an electric field through the box that is inward or outward.

Using Gauss law to determine the charge

To Calculate the electric field, we can use the formula $\overrightarrow{\mathrm{E}}=\frac{\overrightarrow{\mathrm{F}}}{{\mathrm{q}}_{\mathrm{o}}}$, where ${\mathrm{q}}_{\mathrm{o}}$is the test charge. Now after calculating the electric field, we can use Gauss’s law to determine the charge by the formula: $\mathrm{EA}=\frac{{\mathrm{Q}}_{\mathrm{encl}}}{{\mathrm{\epsilon }}_{\mathrm{o}}}$, where A is the area of one side of the box.