Question

Two small insulating spheres with radius 5.00×10−2 m are separated by a large center-to-center distance of 0.600 m . One sphere is negatively charged, with net charge -2.10 μC , and the other sphere is positively charged, with net charge 3.70 μC . The charge is uniformly distributed within the volume of each sphere.

What is the magnitude E of the electric field midway between the spheres?
Take the permittivity of free space to be ϵ0 = 8.85×10−12 C2/(N⋅m2) .

Answer 1

hint:
here is the situation of your problem:

Answer 2

where
\[\begin{gathered}
{Q_1} = 3.70 \times {10^{ - 6}}coulombs \hfill \\
{Q_2} = - 2.10 \times {10^{ - 6}}coulombs \hfill \\
\end{gathered} \]

Answer 3

now the total electric field at midpoint M, is given by the subsequent vector sum:
\[\large {\mathbf{E}}\left( M \right) = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{{Q_1}}}{{{{\left( {d/2} \right)}^2}}}{\mathbf{\hat x}} + \frac{1}{{4\pi {\varepsilon _0}}}\frac{{{Q_2}}}{{{{\left( {d/2} \right)}^2}}}{\mathbf{\hat x}}\]