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Two spherical, nonconducting, and very thin shells of uniformly distributed positive charge $Q$ and radius d are located a distance $10d$ from each other. A positive point charge $q$ is placed inside one of the shells at a distance $d/2$ from the center, on the line connecting the centers of the two shells, as shown in the figure. What is the net force on the charge $q $ ?

$\frac{{qQ}}{{361\pi {\varepsilon _0}{d^2}}}$ to the left
$\frac{{qQ}}{{361\pi {\varepsilon _0}{d^2}}}$ to the right
$\frac{{362qQ}}{{361\pi {\varepsilon _0}{d^2}}}$ to the left
$\frac{{360qQ}}{{361\pi {\varepsilon _0}{d^2}}}$ to the right
Solution

Electric force on charge $q$ due to sphre $A$ is zero.
But electric force due to sphere $B$ on charge $q$ is
$\mathrm{F}=\frac{9 Q}{4 \pi \varepsilon_{0}\left(\frac{19}{2} \mathrm{d}\right)^{2}}$ towards left
$=\frac{\mathrm{qQ}}{361 \pi \varepsilon_{0} \mathrm{d}^{2}}$ towards left