A charge of $8.0 × 10^{-9} C$ is uniformly distributed on the surface of a spherical shell of radius 10 cm. The electric field at a distance of 10 cm from the outer surface of the shell is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $1.8×10^{3} N/C$
Given:
Charge, $Q = 8.0 \times 10^{-9} \ \text{C}$
Radius of shell, $R = 0.1 \ \text{m}$
Distance from outer surface, $d = 0.1 \ \text{m}$
Total distance from center: $r = R + d = 0.1 + 0.1 = 0.2 \ \text{m}$
Electric field outside a spherical shell: $E = \frac{1}{4 \pi \epsilon_0} \frac{Q}{r^2}$
$E = \frac{9 \times 10^9 \cdot 8.0 \times 10^{-9}}{(0.2)^2} = \frac{72}{0.04} = 1800 \ \text{N/C}$
Electric field at 10 cm from outer surface: $E = 1.8 \times 10^3 \ \text{N/C}$