x (a) Determine the electric potential at all points on the z-axis. Assume that the potential goes to zero infinitely far away from the disk. (b) From the potential you found in Part (a), determine the electric field at all points on the z-axis. Make sure that your electric field points in the correct direction above and below the disk.

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1. A disk of radius R has positive charge Q distributed uniformly across its surface. The disk lies flat in
the xy-plane, and the z-axis intersects the disk at its center.
Z
Q
x
y
(a) Determine the electric potential at all points on the z-axis. Assume that the potential goes to
zero infinitely far away from the disk.
(b) From the potential you found in Part (a), determine the electric field at all points on the z-axis.
Make sure that your electric field points in the correct direction above and below the disk.
Transcribed Image Text:1. A disk of radius R has positive charge Q distributed uniformly across its surface. The disk lies flat in the xy-plane, and the z-axis intersects the disk at its center. Z Q x y (a) Determine the electric potential at all points on the z-axis. Assume that the potential goes to zero infinitely far away from the disk. (b) From the potential you found in Part (a), determine the electric field at all points on the z-axis. Make sure that your electric field points in the correct direction above and below the disk.
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Step 1

Solution:

A disc of radius R is uniformly distributed with a positive charge. Given that the charge distribution is uniform the density is uniform. Let us take a small ring ofcharge dq and radius dr. Therefore,

ρ=QπR2=dq2πrdrdq=2QπrdrπR2=2QrdrR2                                                                          .....1

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