Electric Fields with Calculus Video Lessons

Concept

# Problem: A 20-cm-radius ball is uniformly charged to 80nC.(a) What is the ball's volume charge density?(b) How much charge is enclosed by spheres of radii 5, 10, and 20 cm?(c) What is the electric field strength at points 5, 10, 20, 25, and 35 cm from the center?(d) Draw the graph of the charge enclosed, Qencl with the distance r from the center of the sphere for 0&lt;r&lt;35 cm.(e) Draw the graph of the electric field, E(r) with the distance r from the center of the sphere for 0&lt;r&lt;35 cm.

###### FREE Expert Solution

(a)

Volume charge density is given by:

$\overline{){\mathbf{\rho }}{\mathbf{=}}\frac{\mathbf{Q}}{\mathbf{V}}}$Where Q is the charge and V is the volume.

The volume of a sphere:

$\overline{){\mathbf{V}}{\mathbf{=}}\frac{\mathbf{4}}{\mathbf{3}}{\mathbf{\pi }}{{\mathbf{R}}}^{{\mathbf{3}}}}$

Q = 80nC(10-9C/1nC) = 8.0 × 10-8C

R = 20cm(1m/100cm) = 0.20m

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###### Problem Details

A 20-cm-radius ball is uniformly charged to 80nC.
(a) What is the ball's volume charge density?
(b) How much charge is enclosed by spheres of radii 5, 10, and 20 cm?
(c) What is the electric field strength at points 5, 10, 20, 25, and 35 cm from the center?
(d) Draw the graph of the charge enclosed, Qencl with the distance r from the center of the sphere for 0<r<35 cm.
(e) Draw the graph of the electric field, E(r) with the distance r from the center of the sphere for 0<r<35 cm.