Answered: A disk of radius a has a total charge Q…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter26: Electric Potential

Section: Chapter Questions

Problem 27PQ

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Question

A disk of radius a has a total charge Q uniformly distributed over its surface. The disk has negligible thickness and lies in the xy plane. Throughout this problem, you may use the variable k in place of 1/4(pi)E_0.

What is the electric potential V(z) on the z axis as a function of z, for z>0?

What is the magnitude on the z axis as a function of z, for z>0?

Expert Solution

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$(a) L e t u s c o n s i d e r a r i n g w i t h r a d i u s r C h a r g e o n r i n g d q = σ (2 π r) d r . r = \sqrt{z^{2} + r^{2}} (d i s \tan c e o f p o i n t P) S o, V = K e \int_{0}^{R} \frac{σ (2 π r)}{\sqrt{z^{2} + r^{2}}} d r = \frac{2 K e d}{R^{2}} [\sqrt{z^{2} + R^{2}} - z}$

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