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Introductory Physics Homework Help
Calculating Charge on a Spherical Surface with Varying Density
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[QUOTE="BOAS, post: 5001621, member: 488860"] [h2]Homework Statement [/h2] Electric charge resides on a spherical surface of radius 0.3 centered at the origin with charge density specified in spherical polar coordinates by [itex]f(r,\phi, \theta) = 3 × 10^{-12} cos(\theta)[/itex]. Determine the total amount of electric charge on the sphere. [h2]Homework Equations[/h2] Total charge, [itex]Q = \int\limits_s f dA[/itex] [h2]The Attempt at a Solution[/h2] [/B]Essentially, I am confused about why I am finding the answer is zero. What is the physical explanation for this? (provided my maths is ok) Total charge, [itex]Q = \int\limits_s f dA[/itex] [itex]Q = \int\limits_0^{2\pi} \int\limits_0^\pi 3 × 10^{-12} cos(\theta) r^{2} \sin(\theta) d\phi d\theta[/itex] [itex]Q = \int\limits_0^{2\pi} \int\limits_0^\pi 2.7×10^{-13} cos(\theta) \sin(\theta) d\phi d\theta[/itex] [itex] \int\limits_0^{2\pi} d\phi = 2\pi[/itex] [itex]Q = 5.4×10^{-13} \pi \int\limits_0^\pi cos(\theta) \sin(\theta) d\theta[/itex] [itex]\sin(2 \theta) = 2 \sin(\theta) \cos(\theta)[/itex] [itex]\frac{1}{2} \sin(2 \theta) = \sin(\theta) \cos(\theta)[/itex] [itex]Q = 5.4×10^{-13} \pi \int\limits_0^\pi \frac{1}{2} \sin(2 \theta) d\theta[/itex] [itex]Q = 5.4×10^{-13} \pi ((-\frac{1}{4} \cos(2 \pi)) - (-\frac{1}{4}\cos(0)) [/itex] [itex]Q = 0[/itex] I can't see an obvious mistake in my maths, but the answer doesn't seem right either. I really appreciate any help you can give, thanks! [/QUOTE]
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Introductory Physics Homework Help
Calculating Charge on a Spherical Surface with Varying Density
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