Finding Electric Field of a Uniformly Charged Sphere & Plane

AI Thread Summary
The discussion focuses on calculating the electric field of a uniformly charged sphere adjacent to a uniformly charged infinite plane. The user initially finds the electric fields for both the sphere and the plane but doubts the correctness of their results. Another participant points out that the user has incorrectly treated the electric field as a scalar and emphasizes the need to express the electric field vectors in Cartesian coordinates. Additionally, they highlight that the electric field inside the sphere is not uniform, suggesting a reevaluation of the calculations. Clarification on the conditions for the resultant electric field to be at a 45-degree angle is also requested.
matpo39
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ok i was flying through the homework no prob. then i hit this problem and i got an answer but i don't think its right.

A uniformly charged sphere of radius R and volume charge density \rho_0 is adjacent to a uniformly charged infinite plane of surface charge density \sigma_0. the charge densities are related by
\sigma_0=\frac{\rho_0R}{2}
the center of the sphere is a distance d from the plane. Find two points, one inside the sphere and one outside the sphere where the electric field is oriented away from the plane at a 45 degree angle with respect to the z axis.[note these points are not on the axis] (in the figure the infinite plane lies in the xy plane )

well i started this off by finding the electric field inside the sphere

\vec{E_s}=\frac{\rho_0R}{3\epsilon_0}

i then found the charge of the infinite plane via the pill box gaussian surface and came up with
\vec{E_p}=\frac{\sigma_0}{2\epsioln_0}=\frac{\rho_0R}{4\epsilon_0}

\vec{E_s}+\vec{E_p}=\frac{7\rho_0R}{12\epsilon_0}

and breaking to components i got
\frac{7\rho_0R}{12\epsilon_0}(cos45+sin45)

and by a similar approch i got
[\frac{\rho_0R}{\epsilon_0}(\frac{R^2}{3r^2}+\frac{1}{4})](cos45+sin45)

like i said i don't think this is right, so if some one could help me out a bit that would be great

thanks
 
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Mmmh. There's a problem here: you write \vec{E}= \mbox{a scalar}. What are the directions of the E_P and E_S vectors? Write them in cartesian coordinate for a coordinate system centered on the sphere, and find the condition on E_p + E_s to be at 45°.

Oh, and your field equations look wrong. The field inside the sphere is not uniform.
 
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