**From:** Prasad Venugopal (*[email protected]*)

**Date:** Thu May 31 2001 - 15:48:48 PDT

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Although I do not know how all of this applies to the antenna effect ( I need to buy the book ..) I think I know the answer to what Doug meant regarding how a vector changing direction implies acceleration.

Consider any body moving in a straight line with a constant speed and therefore velocity in that direction. A force in a direction perpendicular to the direction of motion tends to change direction without changing the speed. Speed remains the same because the force is perpendicular to direction of motion. The force causes an acceleration to the body by changing the direction without changing the speed. So a vector - speed in a given direction, got accelerated by changing direction without changing magnitude.

ex:

centripetal and centrifugal forces for rotational motion with constant speed. So if you twirl a string with a stone attached to it, the string goes taut and if I remember correctly, the centripetal force is m x v ^2 / r where m is the mass of the stone, v is the velocity and r is the radius. Just so I do not get into trouble, the string has negligible mass :-)

Doug is that correct?

Prasad

-----Original Message-----

From: Sainath Nimmagadda [mailto:[email protected]]

Sent: Thursday, May 31, 2001 2:39 PM

To: Signal Integrity

Subject: [SI-LIST] : Re: Antenna Problem on the Board

Doug,

Thanks for the reference.

Reg the bend, I did not understand your statement that

"A change in direction can also be considered "acceleration" with

vectors".

How do you explain this? Did you use "acceleration" in the d by dt of

velocity sense?

Sainath

Date: Wed, 30 May 2001 19:05:47 -0700

From: "Doug McKean" <[email protected]>

Subject: Re: [SI-LIST] : Re: Antenna Problem on the Board

Sainath Nimmagadda wrote:

*>
*

*> Do you have a book or other reference in mind
*

*> as you connect Laplacian, Maxwell and a conducting bend?
*

Yes and no. The Laplacian/Maxwell derivation which

results in accelerated charge being the mechanism for

radiation is spelled out in a great little book:

Title: "An Introduction to Electromagnetic Wave

Propagation & Antennas"

Author: Shane Cloude

Date: 1995

Publisher: Springer-Verlag New York Inc.

ISBN: 0-387-91501-X

Softcover.

Specifically starting on page 28 and ending on page 30.

The extrapolation from his derivation to a bend in a trace

is mine. Vectors as you're probably well aware are

determined by direction and speed. A change in direction

can also be considered "acceleration" with vectors.

- - Doug McKean

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