Electrostatics — Easy JEE physics MCQ
A solid sphere of radius \(R\) has a uniform volume charge density \(\rho\). The electric field at a distance \(r = R/2\) from the center of the sphere is:
- A. \(\frac{\rho R}{6\varepsilon_0}\)
- B. \(\frac{\rho R}{3\varepsilon_0}\)
- C. \(\frac{\rho R}{2\varepsilon_0}\)
- D. \(\frac{\rho R}{\varepsilon_0}\)
Solution
Using Gauss's law for a point inside a uniformly charged sphere:
For \(r < R\), the electric field is:
\[
E = \frac{\rho r}{3\varepsilon_0}
\]
At \(r = R/2\):
\[
E = \frac{\rho \cdot (R/2)}{3\varepsilon_0} = \frac{\rho R}{6\varepsilon_0}
\]
So the correct option is A.