A sphere of radius carries a positive charge whose volume charge density depends only…

PHYSICS · Single correct · AP · Physics C: Electricity and Magnetism · Electric Charges Fields and Gauss's Law · Electric Charges Fields and Gauss's Law

Problem

A sphere of radius RR carries a positive charge whose volume charge density depends only on the distance rr from the sphere's centre as ρ=ρ0(1−rR)\rho=\rho_0\left(1-\frac{r}{R}\right), where ρ0\rho_0 is a constant. Assume ϵ\epsilon is the permittivity of space. The magnitude of the electric field at distance rr inside the sphere is given by (1) E=ρ0ϵ(r3−r24R)E=\frac{\rho_0}{\epsilon}\left(\frac{r}{3}-\frac{r^2}{4R}\right) (2) E=ρ0ϵ(r4−r23R)E=\frac{\rho_0}{\epsilon}\left(\frac{r}{4}-\frac{r^2}{3R}\right) (3) E=ρ0ϵ(r3+r24R)E=\frac{\rho_0}{\epsilon}\left(\frac{r}{3}+\frac{r^2}{4R}\right) (4) E=ρ0ϵ(r4+r23R)E=\frac{\rho_0}{\epsilon}\left(\frac{r}{4}+\frac{r^2}{3R}\right)

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