- #1
pinkfishegg
- 57
- 3
Hey I was just practicing Gauss's law outside a sphere of radius R with total charge q enclosed. So I know they easiest way to do this is:
∫E⋅da=Q/ε
E*4π*r^2=q/ε
E=q/(4*πε) in the r-hat direction
But I am confusing about setting up the integral to get the same result
I tried
∫ 0 to pi ∫0 to 2pi E*r^2sin(Φ) dΦdΘ for the LHS
i got this from the front of Griffiths where it says:
dl=dr(r-hat)+sdφ d(θ-hat)+rsin(θ)dφ (φ-hat)
But i keep getting 0 when i take this integral sin i get -cos(2π)-cos(0)= -1-(-1)=0
So there's obviously something wrong with my setup. I need to integrate over θ and φ because they are on the surface but I'm not sure about the terms in front. Aren't they supposed to be they ones in front from the dl term?..
Trying to practice this to be able to answer harder questions :P
∫E⋅da=Q/ε
E*4π*r^2=q/ε
E=q/(4*πε) in the r-hat direction
But I am confusing about setting up the integral to get the same result
I tried
∫ 0 to pi ∫0 to 2pi E*r^2sin(Φ) dΦdΘ for the LHS
i got this from the front of Griffiths where it says:
dl=dr(r-hat)+sdφ d(θ-hat)+rsin(θ)dφ (φ-hat)
But i keep getting 0 when i take this integral sin i get -cos(2π)-cos(0)= -1-(-1)=0
So there's obviously something wrong with my setup. I need to integrate over θ and φ because they are on the surface but I'm not sure about the terms in front. Aren't they supposed to be they ones in front from the dl term?..
Trying to practice this to be able to answer harder questions :P