Why Is My Electric Field Calculation for a Conducting Shell Incorrect?

[starving_student]

Consider a thin spherical shell of radius 14.5 cm with a total charge of +39.1 micro coulombs distributed uniformly on its surface. (Take radially outward as the positive direction.)
(b) Find the electric field 39.6 cm from the center of the charge distribution.

Round your answer to three significant figures.

...shouldn't the electric field at this point be given by E = k * (q / r ^ 2), where q is 3.91 x 10 ^ -6 C and r is 0.396 m? Same as a point charge right?
It wants the answer in megaNewtons / Coulomb; I give 2.24 MN/C and it's wrong? Why?

Thanks for any input.

 

[Physics Monkey]

Your formula for the field is certainly correct since the charge is distributed uniformly on the shell and you're looking outside the shell. The only thing I can see is that in your post you say you used the value q = 3.91*10^-6 C when in fact 39.1 micro coulombs would be q = 39.1*10^-6 C. Maybe this is just a typo, or maybe that's your problem.

 

[quicknote]

I can confirm that your understanding of the equation for electric field of a point charge is correct. However, in this scenario, we are dealing with a conducting shell, which has some unique properties that affect the electric field.

Firstly, a conducting shell has an electric field of zero inside the shell. This is due to the fact that the charge on the surface of the shell redistributes itself in such a way that the electric field inside is cancelled out.

Secondly, the electric field outside the conducting shell is the same as that of a point charge located at the center of the shell. This is because the conducting shell acts as a single point charge with the same charge and located at its center.

Therefore, at a distance of 39.6 cm from the center of the shell, the electric field would indeed be given by the equation E = k * (q / r^2), where q is the total charge on the shell and r is the distance from the center. This would result in an electric field of 2.24 MN/C, which is the correct answer.

However, it is important to note that this answer is only valid if the point in question is outside the shell. If the point is inside the shell, the electric field would be zero. So it is important to consider the location of the point when calculating the electric field of a conducting shell.

I hope this clarifies any confusion and helps you understand the concept of electric field in the context of a conducting shell.