A nonconducting sphere 1.3 m in diameter with its center on the x axis at x = 4 m carries a uniform volume charge of density ρ = 4.8 µC/m3. Surrounding the sphere is a spherical shell with a diameter of 2.6 m and a uniform surface charge density σ = -1.2 µC/m2. Calculate the magnitude and direction of the electric field at the following locations.
1) x = 4m, y = 1.2m
2) x = 2m, y = 3m
Both answers are in components of i[hat] and j[hat] vectors with units of N/C.
Well, the textbook solutions use the following equations...
Eshell = kQshell/r2 r[hat]
It uses three different equations for the sphere for each part. Not sure where it got most of these equations as in the textbook itself, these are the equations. I can include the solutions' equations but when I tried their way of solving, my answer was wrong.
Esphere = Qk/r2 (when r is greater than or equal to R)
Esphere = Qkr/R3 (when r is less than or equal to R)
The Attempt at a Solution
I know that the x component of 1) is 0 because that's where the center of the sphere is at. However I'm honestly stumped on how to solve for the y component of 1) and subsequently how to solve 2) in general. As I already mentioned I tried the equations in the textbook solutions but they gave me the wrong answer and didn't explain why they used certain numbers or equations.
For 1), the electric field of the shell is 0 since the point is within the shell. I tried the equations in the textbook itself and I guess (and am absolutely confident this is wrong) the equation for the sphere's electric field is
Esphere = k*ρ*4πr4/R3 r[hat]
I have limited tries on the online homework so detailed help would be greatly appreciated. I tried reading the textbook as well as other textbooks and websites and online videos and I'm still stuck. Thanks.