ch22_p55 - 55 Consider an infinitesimal section of the rod...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 55. Consider an infinitesimal section of the rod of length dx, a distance x from the left end, as shown in the following diagram. It contains charge dq = λ dx and is a distance r from P. The magnitude of the field it produces at P is given by dE = 1 λ dx . 4πε 0 r 2 The x and the y components are dEx = − 1 λ dx sin θ 4πε 0 r 2 1 λ dx cos θ , 4πε 0 r 2 and dE y = − respectively. We use θ as the variable of integration and substitute r = R/cos θ, x = R tan θ and dx = (R/cos2 θ) dθ. The limits of integration are 0 and π/2 rad. Thus, Ex = − and Ey = − λ 4πε 0 R π2 0 λ 4πε 0 R π2 0 sin θdθ = λ cos θ 4πε 0 R π2 0 =− λ 4πε 0 R cosθdθ = − λ sin θ 4πε 0 R π /2 0 =− λ . 4πε 0 R We notice that Ex = Ey no matter what the value of R. Thus, E makes an angle of 45° with the rod for all values of R. ...
View Full Document

This note was uploaded on 01/25/2011 for the course PHYSICS 17029 taught by Professor Rebello,nobels during the Fall '10 term at Kansas State University.

Page1 / 2

ch22_p55 - 55 Consider an infinitesimal section of the rod...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online