JEE Main · PhysicsHard
A solid non-conducting sphere of radius $R$ has a volume charge density $\rho$ that varies with distance $r$ from the center as $\rho = \rho_0 (r/R)$. The electric field at a distance $r = R/2$ from the center is given by:
- A.$\frac{\rho_0 R}{24 \epsilon_0}$
- B.$\frac{\rho_0 R}{12 \epsilon_0}$
- C.$\frac{\rho_0 R}{8 \epsilon_0}$
- D.$\frac{\rho_0 R}{6 \epsilon_0}$
Show correct answer & step-by-step solution
Correct answer: A — $\frac{\rho_0 R}{24 \epsilon_0}$
Solution
Use Gauss Law by integrating the charge density over the volume of a sphere of radius . The enclosed charge is . Applying Gauss Law yields .
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