Electric Fields with Calculus Video Lessons

Concept

# Problem: Charge Q is distributed uniformly throughout the volume of an insulating sphere of radius R = 4.00 cm. At a distance of r = 8.00 cm from the center of the sphere, the electric field due to the charge distribution has magnitude 640 N/C.Part A. What is the volume change density for the sphere?Express your answer to two significant figures and include the appropriate units.Part B. What is the magnitude of the electric field at a distance of 2.00 cm from the sphere’s center?Express your answer to two significant figures and include the appropriate units

###### FREE Expert Solution

In this problem, we have a uniformly charged insulating sphere with a radius of 4cm. We are interested in a point inside and outside the sphere.

The necessary equations are:

The electric field outside the sphere (r > R where R is the radius of the sphere):

$\overline{){\mathbf{E}}{\mathbf{=}}\frac{\mathbf{k}\mathbf{Q}}{{\mathbf{r}}^{\mathbf{2}}}}$

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###### Problem Details

Charge Q is distributed uniformly throughout the volume of an insulating sphere of radius R = 4.00 cm. At a distance of r = 8.00 cm from the center of the sphere, the electric field due to the charge distribution has magnitude 640 N/C.

Part A. What is the volume change density for the sphere?
Express your answer to two significant figures and include the appropriate units.

Part B. What is the magnitude of the electric field at a distance of 2.00 cm from the sphere’s center?
Express your answer to two significant figures and include the appropriate units