Question

Two 2.0-cm-diameter insulating spheres have a 6.60 cm space between them. One sphere is charged to + 76.0 nC , the other to - 30.0 nC . Part A What is the electric field strength at the midpoint between the two spheres? Express your answer with the appropriate units.

Answer 1

Answer:

$5.2\times 10^5N/C$

Explanation:

Since the two charged bodies are symmetric, we can calculate the electric field taking both of them as point charges.

This can be easily seen if we use Gauss's law, $\int{E} \, dA=\frac{Q_{enclosed}}{\epsilon_o}$

We take a larger sphere of radius, say r, as the Gaussian surface. Then the electric field due to the charged sphere at a distance r from it's center is given by,

$E=\frac{1}{4\pi r^2} \frac{Q_{enclosed}}{\epsilon_o}$

which is the same as that of a point charge.

In our problem the charges being of opposite signs, the electric field will add up. Therefore,

$E_{total}=\frac{1}{4\pi\epsilon_o}\frac{q_1+q_2}{r^2}= (9\times10^9) \frac{(76+30)\times10^{-9}}{((1+3.3)\times10^{-2})^2}N/C =5.2\times10^5N/C$

where, $r$ = distance between the center of one sphere to the midpoint (between the 2 spheres)