Given, charge q1=+2µC, charge q2=+8µC and distance between the charges d=15cm. As, the electric field is zero at point p only if the field due to charge +2µC balances the field due to charge +8µC Let x be the distance from charge q1 at which the electric field is zero as shown in the figure below.
∴
kq1
x2
=
kq2
(15−x)2
⇒
1
4πε0
⋅
2×10−6
x2
=
1
4πε0
8×10−6
(15−x)2
⇒
1
x2
=
4
(15−x)2
∴
1
x
=
2
15−x
⇒2x=15−x ⇒x=5cm Thus, the required point is at a distance of 5cm from 2µC.