3- A positive charge q is uniformly distributed over the area of a disk, of radius R, placed horizontally on the x-y plane as shown in the figure. a) Find an expression for the charge density o. b) Find an expression for the electric potential at a point P on the axis passing through the center of the disk and at a distance z from its center. c) Check that your formula is consistent with what you would expect for the case when z→ ± 0
3- A positive charge q is uniformly distributed over the area of a disk, of radius R, placed horizontally on the x-y plane as shown in the figure. a) Find an expression for the charge density o. b) Find an expression for the electric potential at a point P on the axis passing through the center of the disk and at a distance z from its center. c) Check that your formula is consistent with what you would expect for the case when z→ ± 0
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Transcribed Image Text:3- A positive charge q is uniformly distributed over the
area of a disk, of radius R, placed horizontally on the
x-y plane as shown in the figure.
a) Find an expression for the charge density o.
b) Find an expression for the electric potential at a point
P on the axis passing through the center of the disk
and at a distance z from its center.
c) Check that your formula is consistent with what you
would expect for the case when z →± ∞
R
dr
10
r
√² + z²
Hint: Divide the disk into ring shaped elements, each of area da = 2ër dr, then integrate over r
(from r=0 till r=R).
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