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?
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.
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?
It seems like you are using the correct formula, but let's go through the calculations to double-check. The formula you have mentioned, E = k_e(Q/r^2), is indeed the correct equation for calculating the magnitude of the electric field due to a point charge.
Given:
Charge, Q = 8 pC = 8 × 10^(-12) C (convert pC to C)
Distance from the center, r = 2.6 cm = 2.6 × 10^(-2) m (convert cm to m)
k_e = 8.98755 × 10^9 N*m^2/C^2 (Coulomb's constant)
Substituting the values into the equation:
E = k_e(Q/r^2)
E = 8.98755 × 10^9 N*m^2/C^2 * (8 × 10^(-12) C) / (2.6 × 10^(-2) m)^2
Simplifying the equation:
E = 8.98755 × 8 × (10^9 × 10^(-12)) N*m^2/C^2 / (2.6 × 10^(-2))^2 m^2
E = 71.9004 N*m^2/C^2 / (2.6 × 10^(-2))^2 m^2
E ≈ 71.9004 N * (1 / (2.6 × 10^(-2))^2) C
E ≈ 71.9004 N * (1 / (6.76 × 10^(-4))) C
E ≈ 71.9004 N * 1476.89 C
E ≈ 106,361.4564 N/C
Based on the calculations, the magnitude of the electric field 2.6 cm from the center of the charged surfaces should be approximately 106,361.46 N/C. It appears that you have obtained the correct answer.
If your answer is marked as incorrect, then there might be another factor or step involved in the problem that has not been mentioned. Double-check any additional instructions or information provided in the question to make sure you have considered everything.