P30_015

# P30_015 - a 2 R = a √ a 2 4 x 2 multiplies the expression...

This preview shows page 1. Sign up to view the full content.

15. We imagine the square loop in the yz plane (with its center at the origin) and the evaluation point for the Feld being along the x axis (as suggested by the notation in the problem). The origin is a distance a/ 2 from each side of the square loop, so the distance from the evaluation point to each side of the square is, by the Pythagorean theorem, R = p ( a/ 2) 2 + x 2 = 1 2 p a 2 +4 x 2 . Only the x components of the Felds (contributed by each side) will contribute to the Fnal result (other components cancel in pairs), so a trigonometric factor of
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: a/ 2 R = a √ a 2 + 4 x 2 multiplies the expression of the Feld given by the result of problem 11 (for each side of length L = a ). Since there are four sides, we Fnd B ( x ) = 4 µ µ i 2 πR ¶µ a √ a 2 + 4 R 2 ¶µ a √ a 2 + 4 x 2 ¶ = 4 µ i a 2 2 π ( 1 2 )( √ a 2 + 4 x 2 ) 2 p a 2 + 4( a/ 2) 2 + 4 x 2 which simpliFes to the desired result. It is straightforward to set x = 0 and see that this reduces to the expression found in problem 12 (noting that 4 √ 2 = 2 √ 2)....
View Full Document

## This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

Ask a homework question - tutors are online