1) Assume we have a thin conducting ring (radius R) that is uniformly charged with net charge Q. We'regoing to derive an equation for the electric field along the axis going through the center of the ring.Choose the z axis to coincide with the axis extending vertically through the middle of the ring.Rith "bit"Charged ring(Image from textbook by T.A. Moore)a) Explain why the net electric field at the center of the ring (in the plane of the ring) is zerob) We want to slice the ring into tiny charged "bits". Explain why (show mathematically) that thecharge in the "ith bit", q; is:qi =,A02nc) Find an equation for |E (the magnitude of the electric field) at point P, that is caused by q: interms of Q, 8o, A¢, R, and z (the z coordinate of point P).d) Now you've calculated the magnitude of the electric field contributed by one bit of charge.Explain why when you add in all the bits of charge from the entire ring, the total electric fieldmust point straight up along the z-axis.e) Now do the summation and show that:1Qz4TE0(R² + z?)³/z²f) If the radius of the ring was doubled in size, but the charge Q remained the same, what wouldbe the ratio the new linear charge density to the original linear charge density?P.

Answered: Image /qna-images/answer/334b6aa0-e812-4d10-9b67-e445776292e0.jpg

1) Assume we have a thin conducting ring (radius R) that is uniformly charged with net charge Q. We're going to derive an equation for the electric field along the axis going through the center of the ring. Choose the z axis to coincide with the axis extending vertically through the middle of the ring. R ith "bit" Charged ring (Image from textbook by T.A. Moore) a) Explain why the net electric field at the center of the ring (in the plane of the ring) is zero b) We want to slice the ring into tiny charged "bits". Explain why (show mathematically) that the charge in the "ith bit", q; is: 2n c) Find an equation for |E (the magnitude of the electric field) at point P, that is caused by q; in terms of Q, Eg, Aø, R, and z (the z coordinate of point P). P.

1) Assume we have a thin conducting ring (radius R) that is uniformly charged with net charge Q. We're going to derive an equation for the electric field along the axis going through the center of the ring. Choose the z axis to coincide with the axis extending vertically through the middle of the ring. R ith "bit" Charged ring (Image from textbook by T.A. Moore) a) Explain why the net electric field at the center of the ring (in the plane of the ring) is zero b) We want to slice the ring into tiny charged "bits". Explain why (show mathematically) that the charge in the "ith bit", q; is: 2n c) Find an equation for |E (the magnitude of the electric field) at point P, that is caused by q; in terms of Q, Eg, Aø, R, and z (the z coordinate of point P). P.

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter5: Electric Charges And Fields

Section: Chapter Questions

Problem 101P: In this exercise, you practice electric field lines. Make sure you represent both the magnitude and...

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Concept explainers

Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

Question

1) Assume we have a thin conducting ring (radius R) that is uniformly charged with net charge Q. We're
going to derive an equation for the electric field along the axis going through the center of the ring.
Choose the z axis to coincide with the axis extending vertically through the middle of the ring.
R
ith "bit"
Charged ring
(Image from textbook by T.A. Moore)
a) Explain why the net electric field at the center of the ring (in the plane of the ring) is zero
b) We want to slice the ring into tiny charged "bits". Explain why (show mathematically) that the
charge in the "ith bit", q; is:
qi =,A0
2n
c) Find an equation for |E (the magnitude of the electric field) at point P, that is caused by q: in
terms of Q, 8o, A¢, R, and z (the z coordinate of point P).
d) Now you've calculated the magnitude of the electric field contributed by one bit of charge.
Explain why when you add in all the bits of charge from the entire ring, the total electric field
must point straight up along the z-axis.
e) Now do the summation and show that:
1
Qz
4TE0(R² + z?)³/z²
f) If the radius of the ring was doubled in size, but the charge Q remained the same, what would
be the ratio the new linear charge density to the original linear charge density?
P.

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