   Chapter 11.11, Problem 36E

Chapter
Section
Textbook Problem

# A uniformly charged disk has radius R and surface charge density σ as in the figure. The electric potential V at a point P at a distance d along the perpendicular central axis of the disk is V = 2 π k e σ ( d 2 + R 2 − d ) where ke is a constant (called Coulomb’s constant). Show that V ≈ π k e R 2 σ d   for   large   d To determine

To show: The Electric Potential VπkeR2σd,for large d.

Explanation

Given:

The radius of the disk is R.

Density is denoted by σ.

The electric potential along the perpendicular central axis of the disk is V=2πkeσ(d2+R2d) d, where ke is called Coulomb’s constant.

Calculation:

Given that, V=2πkeσ(d2+R2d).

Expand the term d2+R2 as follows.

d2+R2=d2(1+R2d2)=d(1+R2d2)12=d(1+R22d2+)<

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