Two small spherical shells A and B are given positive charges of 9 C and 4 C respectively and placed such that their centres are separated by 10m. If P is a point in between them, where the electric field intensity is zero, then the distance of the point P from the centre of A is 

At the point P electric field intensity is zero.
So, the electric field intensity' due to both charges are equal and opposite. 
Let distance of q₁ charge from point P is r.
So, distance of q₂ charge from; point P is (10 $-$ r).

$\frac{1}{4\pi {\epsilon }_0}\frac{q_1}{r^2}=\frac{1}{4\pi {\epsilon }_0}\frac{q_2}{(10-r{)}^2}$

$\Rightarrow \frac{q_1}{r^2}=\frac{q_2}{(10-r{)}^2}$        

$\Rightarrow \frac{9}{r^2}=\frac{4}{(10-r{)}^2}$     $\left(\because q_1=9\mathrm{C},q_2=4\mathrm{C}\right)$

$\Rightarrow {\left(\frac{3}{r}\right)}^2={\left(\frac{2}{10-r}\right)}^2$

$\Rightarrow \frac{3}{r}=\frac{2}{10-r}$

$\Rightarrow 3(10-r)=2r$

$\Rightarrow 30-3r=2r$

$\Rightarrow 5r=30\Rightarrow r=6 \mathrm{m}$