A charge of 8 pC is uniformly distributed throughout the volume between concentric spherical surfaces having radii of 1.7 cm and3.7 cm. What is the magnitude of the electric field 2.6 cm from the center of the surfaces?

Question

A charge of 8 pC is uniformly distributed throughout the volume between concentric spherical surfaces having radii of 1.7 cm and3.7 cm. What is the magnitude of the electric field 2.6 cm from the center of the surfaces?
Let k_e=8.98755*10^9 N*m^2/C^2

I used the formula
E=k_e(Q/r^2) because the distance is greater than the inner sphere; however, the answer I'm getting 106.362 N/C is supposedly wrong.

Am I using the wrong formula or what?

drwls · Answer

r = 2.6 cm from the center is between the inner and the outer spheres. You got that right. Not all of the Q is inside the r = 2.6 cm radius, however.

The total Q you should use in your equation is 8 pC*
(2.6^2-1.7^2)/(3.7^2-1.7^2)
= 8 pC*0.3583
since the charge is uniformly distributed between the spheres.

alex · Answer

Okay, when I took the quotient of the distance - r1 and r2-r1, I got 0.45

Then multiplied by Q gave me 3.6*10^-12 (I changed pC to C).

Am I doing something wrong again? How did you come up with 0.3583?