Question

charge of −26μC is distributed uniformly throughout a spherical volume of radius 10.0

cm. Determine the electric field due to this charge at a distance of (a) 3.0 cm, (b) 10.0

cm, and (c) 20.0 cm from the center of the sphere.

Ans: a)6.2e-5/ε N/C

b)2.067e-4/ε N/C

c)5.17e-4/ε N/C

looking for detail steps/wants to know where you got the equations from.

Answer 1

Solution) Q = - 26 uC = - 26×10^(-6) C

R = 10 cm = 0.1 m

(a) r = 3 cm = 0.03 m

E = ?

E = (Qr)/(4(pi)(epsilonnot)(R^3))

E = ((26×10^(-6))(0.03))/(4(pi)(epsilonnot)(0.1^3))

E = (6.2×10^(-5))/(epsilonnot) N/C

In simplified form

E = 7020×10^(3) N/C

(b) r = 10 cm = 0.1 m

E = (Q)/(4(pi)(epsilonnot)(r^2))

E = (26×10^(-6))/(4(pi)(epsilonnot)(0.1^2))

E = (2.067×10^(-4))/(epsilonnot) N/C

In simplified form

E = 0.233×10^(8) N/C

(C) r = 20 cm = 0.2 m

E = (Q)/(4(pi)(epsilonnot)(r^2))

E = (26×10^(-6))/(4(pi)(epsilonnot)(0.2^2))

E = (5.17×10^(-4))/(epsilonnot) N/C

In simplified form

E = 0.583×10^(8) N/C