A charge Q is distributed within a sphere of radius R. Calculate everywhere the electric field and the potential in the case the charge density varies as p(x) = PO where x is the distance from the center of the sphere and x ≤ R. Also, how does the result compare with the case of uniform density?
A charge Q is distributed within a sphere of radius R. Calculate everywhere the electric field and the potential in the case the charge density varies as p(x) = PO where x is the distance from the center of the sphere and x ≤ R. Also, how does the result compare with the case of uniform density?
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
Transcribed Image Text:A charge Q is distributed within a sphere of radius R. Calculate
everywhere the electric field and the potential in the case the charge
density varies as
p(x) = PO
where x is the distance from the center of the sphere and x ≤R. Also,
how does the result compare with the case of uniform density?
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Step 1: Know the concept:
VIEWStep 2: Draw a diagram showing gaussian surfaces and find the left side of equation (1):
VIEWStep 3: Find the electric field inside the sphere:
VIEWStep 4: Find the electric field outside the sphere:
VIEWStep 5: Find the electric potential outside the sphere:
VIEWStep 6: Find the electric potential inside the sphere:
VIEWStep 7: Comparison of result with that of the uniform charge distribution:
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