Question

Figure shows, in cross section, two solid spheres with uniformly distributed charge throughout their volumes. Each has radius $R$, Point $P$ lies on a line connecting the centres of the spheres, at radial distance $R/2$ from the centre of sphere $1$. If the net electric field at point $P$ is zero and $Q_1$ is $64\mu \text{C}$. What is $Q_2$ in $\mu \text{C}$

Answer 1

Given:
Electric field at $P$ is zero. Therfore electric field due to Sphere $1$ and sphere $2$ is equal and opposite.
$\therefore E_1=E_2$
For $Q_1$, point $P$ is inside the sphere and for $Q_2$ it is outside of sphere.

$\frac{Kqr}{R^3}=\frac{Kq}{r^2}$

$\Rightarrow \frac{K{Q}_1\frac{R}{2}}{R^3}=\frac{K{Q}_2}{{\left(\frac{3R}{2}\right)}^2}$

$\Rightarrow Q_1=\frac{8}{9}\times Q_2$

$\Rightarrow 64=\frac{8}{9}\times Q_2$

$\Rightarrow Q_2=72\mu \text{C}$