Question

The electric field inside a nonconducting sphere of radius $R$, with charge spread uniformly throughout its volume, is radially directed and has magnitude $$E(r)=|\vec{E}(r)|=\frac{|q| r}{4 \pi \varepsilon_{0} R^{3}}.$$ Here $q$ (positive or negative) is the total charge within the sphere, and $r$ is the distance from the sphere's center. (a) Taking $V=0$ at the center of the sphere, find the electric potential $V(r)$ inside the sphere. (b) What is the difference in electric potential between a point on the surface and the sphere's center? (c) If $q$ is positive, which of those two points is at the higher potential?

          The electric field inside a nonconducting sphere of radius $R$, with charge spread uniformly throughout its volume, is radially directed and has magnitude
$$E(r)=|\vec{E}(r)|=\frac{|q| r}{4 \pi \varepsilon_{0} R^{3}}.$$ Here $q$ (positive or negative) is the total charge within the sphere, and $r$ is the distance from the sphere's center. (a) Taking $V=0$ at the center of the sphere, find the electric potential $V(r)$ inside the sphere. (b) What is the difference in electric potential between a point on the surface and the sphere's center? (c) If $q$ is positive, which of those two points is at the higher potential?

Added by Patricia H.

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