• Support PF! Buy your school textbooks, materials and every day products Here!

Magnetic Field of a current distribution

  • Thread starter motu miah
  • Start date
  • #1
1
0

Homework Statement



A magnetic lens is made by placing four long, thin current carrying conducting sheets of width ##2a## on the sides of a square, as shown in the figure. The currents in the conducting sheets are distributed uniformly over the sheets, and are directed either into or out of the plane of the page, as shown in the figure. You may neglect the effects of ends and corners.

Capture.jpg


(a) What are the values of ##H_{x}(a^{-},y)## and ##H_{y}(a^{-},y)## along the boundary just to the left of the current sheet at ##x=a##? Likewise, what are the values of ##H_{x}(x,a^{-})## and ##H_{y}(x,a^{-})## along the upper boundary just below the current sheet at ##y=a##?

(b) What are ##H_{x}## and ##H_{y}## at the origin?

(c) Find ##H_{x}## and ##H_{y}## in the interior region ##-a<x<a## and ##-a<y<a##?

(d) Derive the equation which describes the field lines in the interior region.

(e) Suppose that a beam of positively charged particles is injected into the interior region of the lens so that their velocities are initially along the ##z##-axis (out of the page). Discuss how the lens can act to focus the beam. Try to be as quantitative as possible.

Homework Equations



The Attempt at a Solution



(a) ##H_{x}(a^{-},y) = 0## and ##H_{y}(a^{-},y) = \frac{\mu_{0}I}{2\pi a^{-}}##.

##H_{x}(x,a^{-}) = \frac{\mu_{0}I}{2\pi a^{-}}## and ##H_{y}(x,a^{-}) = 0##.

Please check my answers to (a).
 

Answers and Replies

  • #2
18,086
7,507
Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

Related Threads on Magnetic Field of a current distribution

Replies
6
Views
206
Replies
13
Views
6K
Replies
2
Views
2K
Replies
1
Views
343
Replies
0
Views
5K
  • Last Post
Replies
0
Views
1K
Replies
12
Views
2K
Replies
1
Views
2K
Top