I disagree with the answers for this AP physics 2 question, please help explain?

JonathanCWalker

70. A hollow metal sphere 1.0m in diameter carries a charge of 4.0 "u" C. The electric field at a distance of 2.0m from the center of the sphere is most nearly
a. 9.0 x 10^3 N/C
b. 1.8 x 10^4 N/C
c. 2.4 x 10^4 N/C
d. 3.6 x 10^4 N/C
e. 1.4 x 10^5 N/C

The sphere has a radius of .5 m, so shouldn't the electric field be calculated from (1.5 m), which is the distance of the nearest excess charge to the point? Why must we calcuate taking r as 2.0 when there is no charge at the point in the center of the sphere?

Taking r to be 1.5, I get an answer of approx. 1.6 x 10^4 N/C

Thank you for your help.

topsquark

Forum Staff
70. A hollow metal sphere 1.0m in diameter carries a charge of 4.0 "u" C. The electric field at a distance of 2.0m from the center of the sphere is most nearly
a. 9.0 x 10^3 N/C
b. 1.8 x 10^4 N/C
c. 2.4 x 10^4 N/C
d. 3.6 x 10^4 N/C
e. 1.4 x 10^5 N/C

The sphere has a radius of .5 m, so shouldn't the electric field be calculated from (1.5 m), which is the distance of the nearest excess charge to the point? Why must we calcuate taking r as 2.0 when there is no charge at the point in the center of the sphere?

Taking r to be 1.5, I get an answer of approx. 1.6 x 10^4 N/C

Thank you for your help.
For a symmetric problem like this the field acts as if all the charge is concentrated at the "center of charge" which is simply the center of the sphere in this case. So r = 2.0 m.

(Actually, using Gauss' Law we can say this "center of charge" feature holds for any Gaussian surface completely surrounding the charge distribution.)

-Dan

benit13