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**1. The problem statement, all variables and given/known data**

There is a charged dielectric sphere of radius R. I center it at the origin of an x,y,z cartesian system. It has a charge density rho=3Qcos(theta)/4*Pi*R^3. Q and R are given.

I need to find the Electric field at a point that is outside the sphere.

**2. Relevant equations**

int(E*dA)=Q_in/Epsilon0

**3. The attempt at a solution**

int(E*dA)=Q_in/Epsilon0

E(4*Pi*r^2)=(rho)(4/3)*Pi*r^3)/epsilon0

E=3Qcos(theta)r/12*Pi*epsilon0*R^3 in the r-hat direction

Is this right? Dont I have to figure out the field in the x-hat, y-hat, and z-hat directions? How does this work if my E is in the r-hat direction?

Thanks in advance!