MHT CET · Physics · Electrostatics
The electric field intensity on the surface of a solid charged sphere of radius \(r\) and volume charge density \(\sigma\) is ( \(\epsilon_0=\) permittivity of free space)
- A zero
- B \(\frac{5 \sigma r}{6 \epsilon_0}\)
- C \(\frac{1}{4 \pi \epsilon_0} \frac{\sigma}{r}\)
- D \(\frac{\sigma r}{3 \epsilon_0}\)
Answer & Solution
Correct Answer
(D) \(\frac{\sigma r}{3 \epsilon_0}\)
Step-by-step Solution
Detailed explanation
\(Q = \sigma V = \sigma \left( \frac{4}{3} \pi r^3 \right)\) \(E = \frac{1}{4 \pi \epsilon_0} \frac{Q}{r^2} = \frac{1}{4 \pi \epsilon_0} \frac{\sigma \left( \frac{4}{3} \pi r^3 \right)}{r^2} = \frac{\sigma r}{3 \epsilon_0}\)
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