Using the exact expression for the electric field a uniformly charged disk (on the equation sheet) in the yz-plane at x = 0 with total charge +5.00 µC and radius 2.50 cm. (a) What is the surface charge density of the disk? (b) What is the electric field (both magnitude and direction) and a point 1.00 mm from the center of the disk along the symmetry axis of the disk, i.e., at x = 1.00 mm? (c) If we treat the uniformly charged disk as a uniformly charged, infinite plane (again on the equation sheet located in the yz-plane at x = 0), then what is the electric field at a distance of 1.00 mm from the plane, i.e., at x = 1.00 mm? Comment on how close this value is to the exact value calculated in (b). (d) Starting with the exact expression
Using the exact expression for the electric field a uniformly charged disk (on the equation sheet) in the yz-plane at x = 0 with total charge +5.00 µC and radius 2.50 cm. (a) What is the surface charge density of the disk? (b) What is the electric field (both magnitude and direction) and a point 1.00 mm from the center of the disk along the symmetry axis of the disk, i.e., at x = 1.00 mm? (c) If we treat the uniformly charged disk as a uniformly charged, infinite plane (again on the equation sheet located in the yz-plane at x = 0), then what is the electric field at a distance of 1.00 mm from the plane, i.e., at x = 1.00 mm? Comment on how close this value is to the exact value calculated in (b). (d) Starting with the exact expression
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Transcribed Image Text:Using the exact expression for the electric field a uniformly charged disk (on the equation
sheet) in the yz-plane at x = 0 with total charge +5.00 µC and radius 2.50 cm. (a) What is the
surface charge density of the disk? (b) What is the electric field (both magnitude and
direction) and a point 1.00 mm from the center of the disk along the symmetry axis of the
disk, i.e., at x 1.00 mm? (c) If we treat the uniformly charged disk as a uniformly charged,
infinite plane (again on the equation sheet located in the yz-plane at x = 0), then what is the
electric field at a distance of 1.00 mm from the plane, i.e., at x = 1.00 mm? Comment on how
close this value is to the exact value calculated in (b). (d) Starting with the exact expression
for the electric field of a uniformly charged disk (on the equation sheet) show that in the limit
as x <<R you obtain the exact expression for the electric field of a uniformly charged,
infinite plane. Be sure to show the steps in your derivation, and to only use symbols (not
numeric values). (e) Include a diagram of the situation.
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