## Spheres, Plates, and Gauss' Law

1. The problem statement, all variables and given/known data

A sphere of radius 8.0 cm carries a uniform volume charge density rho = 500*10^-9 C/m^3. What is the electric field at r = 3.0 cm?

a.36.0 N/C

b.230 N/C

c.140 N/C

d.565 N/C

e.450 N/C

2. Relevant equations

E = (k*Q*r)/(R^3), where R = sphere’s radius and r is distance inside sphere

3. The attempt at a solution
V = (4/3)*pi*(0.08 m)^3 = 0.00214 m^3
Q = p*V = (500*10^-9 C/m^3)*(0.00214 m^3) = 1.07*10^-9 C

E = (k*Q*r)/(R^3), where R = sphere’s radius and r is distance inside sphere

E = (8.988*10^9)*(1.07*10^-9 C)/(0.03 m^2) = 564.7 N/C

1. The problem statement, all variables and given/known data

A large, flat conducting plate has a surface charge density sigma = 8.0*10^-9 C/m^2 on one of its surfaces. What is the magnitude of the electric field 10 µm from this plate?

a.72 N/C

b.0.23 kN/C

c.0.90 kN/C

d.90 MN/C

e.9.0 1012 N/C

2. Relevant equations

electric flux = Integral[E*A] = Q_enclosed/epsilon_0

3. The attempt at a solution

E*A_plate = q/epsilon_0
E*A_plate = (sigma*A_plate)/(epsilon_0)

E = sigma/epsilon_0 = (8.0*10^-9 C/m^2)/(8.85*10^-12) = 904 N/C

Thanks.
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 Admin Correct in both cases! For future reference - http://hyperphysics.phy-astr.gsu.edu...elesph.html#c4 and http://hyperphysics.phy-astr.gsu.edu...elesht.html#c1 Note that the second problem states "surface charge density sigma . . . . on one of its surfaces."