Question

A uniformly charged sphere is placed inside a charged hollow sphere as shown in the figure. $O$ is the centre of hollow sphere and $C$ is the centre of solid sphere. The magnitude of charge on both the spheres is $4\left(\sqrt{\frac{3}{7}}\right) \mu C$. The electric field at point $P$ which lies just outside the hollow sphere is given by $3 \alpha K N / C$. Find the value of $\alpha$. (Here, $K=\frac{1}{4 \pi \varepsilon_{0}}$ )

Answer 1

$E_{r}=\vec{E}_{1}+\vec{E}_{2}$
$E_{r}=\sqrt{E_{1}^{2}+E_{2}^{2}+2 E_{1} E_{2} \cos \theta}$
where, $E_{1}=\frac{k Q}{1^{2}}, E_{2}=\frac{K Q}{(\sqrt{4})^{2}}$
and $\theta=60^{\circ}$