Potential & dipole moment

[fordo]

This is from a sample problem from an old text book The answers are given for all 4 parts.
I've worked the problem and have shown all my work in detail in the attachment. My answers agree with the text book except for part (d). Text book gives an answer of 1.597 V but I come up with 1.377 V. I believe I'm doing something wrong or cannot find a simple arithmetic error. This is not a rounding error. Can anybody find the mistake?

Some notes and definitions from the text (Engineering Electromagnetics, Hayt, 4rth edition)

p is the dipole moment and d is the distance that separates the two equal and opposite charges of the dipole.


r is the vector from the origin to the to the field point and r¢ is the vector from the origin to the center of the dipole.

The problem, page 118 D 4.9:

A dipole at the origin in free space has a moment of 400pe0(0.6ax – 0.75ay + 0.8az) C•m. Find the potential at:
(a) PA(0, 0, 5)

(b) PB(0, 5, 0)

(c) PC(5, 0, 0)

(d) PD(2, 3, 4)

 

[MrAl]

Hi,

Your math looks correct in that the math itself is correct. Where did you get the 'formula' for this? Maybe we are not interpreting it correctly.
I have seen many book answers incorrect so it wouldnt be the first time.

 

[fordo]

The formula comes right out of the book I mentioned earlier: Engineering Electromagnetics, Hayt, 4rth edition.

Here’s a link to a newer version that shows the main formula I used (but doesn’t have this specific sample problem):

https://www.electro-tech-online.com/custompdfs/2011/12/chapt04.pdf

See page 108 formula #39.

Like you, I’m thinking the answer might be a typo, but then again maybe I’m just making some subtle little mistake and can’t see it.

By the way, I’m not a student; just an EE who never had a solid grasp of Maxwell’s equations and pursue this as a pass time (geek???).

Thanks for looking.

 

[Ratchit]

fordo and MrAl,

The formula is correct. It is an approximation that assumes r' >> d .

Ratch

 

[MrAl]

Hi again,

Ratch:
ok thanks.

fordo:
What i didnt like was that the first three examples were degenerate vector cases so i didnt want to base any go/no go decision based on those alone, and the fourth example was a better example but we didnt have anything to compare it with. Since you've posted the text however we can double check by doing their example which is similar to the fourth example in your original text. Doing that and using the same procedure, we get the same answer.
This means that the original textbook answer was not correct and you got the right answer for that fourth problem.

 

[fordo]

Thanks again

I appreciate the feedback.