Question

A metal sphere with its centre at A and radius R has a charge 2q on it. The field at a point B outside the sphere is E. If another metal sphere of radius 3R and having a charge -3q is placed with its cnetre at point B, then resultant electric field at a point mid way between A and B will be

• A. 0.5E
• B. 2E
• C. 2.5E
• D. 10E

Answer 1

The correct option is D 10E

$E=\frac{1}{4\pi {ϵ}_0}\frac{2q}{d^2}--------\left(1\right)$
$E_R=E_A+E_B=\frac{1}{4\pi {ϵ}_0}\frac{4}{d^2}[2q+3q]$
$E_R=\frac{1}{4\pi {ϵ}_0}\frac{4\pi 5q}{d^2}=\frac{1}{4\pi E_0}\frac{20q}{d^2}------\left(2\right)$
$\frac{\left(2\right)}{\left(1\right)}\frac{ER}{E}=\frac{20}{2}=10;E_R=10E$