A uniformly charged sphere of 80 μC and radius 2 cm is placed in the air. The electric field intensity at a point 20 cm from the center of the sphere is

$1.80 × 10^7 N/C$

The correct answer is Option (1) → $1.80 × 10^7 N/C$

Given:

Total charge, $Q = 80\ \mu\text{C} = 80 \times 10^{-6}\ \text{C}$

Radius of sphere, $R = 2\ \text{cm} = 0.02\ \text{m}$

Point outside the sphere at $r = 20\ \text{cm} = 0.2\ \text{m}$

Electric field outside a uniformly charged sphere behaves like a point charge:

$E = \frac{1}{4 \pi \epsilon_0} \frac{Q}{r^2}$

Substitute values:

$E = \frac{9 \times 10^9 \cdot 80 \times 10^{-6}}{(0.2)^2} = \frac{720 \times 10^3}{0.04} = 18 \times 10^6\ \text{V/m}$

∴ Electric field at 20 cm from center = $1.8 \times 10^7\ \text{V/m}$