The Pythagorean Theorem: Solved Problem, Exercises of Electrical Engineering

Prof. Gulzarilal Shroff suggested this solution to problem related to Electrical Engineering course at Jaypee University of Engineering and Technology. It includes: Gauss, Law, Magnetism, Enclosed, Surface, Cylinder, Magnet, Bar, Field, Lines

Typology: Exercises

2011/2012

Uploaded on 07/20/2012

sharman
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6. (a) The Pythagorean theorem leads to
B=B2
h+B2
v=µ0µ
4πr3cos λm2
+µ0µ
2πr3sin λm2
=µ0µ
4πr3cos2λm+4sin
2λm=µ0µ
4πr31 + 3 sin2λm,
where cos2λm+ sin2λm=1wasused.
(b) We use Eq. 3-6:
tan φi=Bv
Bh
=(µ0µ/2πr3) sin λm
(µ0µ/4πr3)cosλm
=2tanλm.
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  1. (a) The Pythagorean theorem leads to

B =

B

2 h

+ B

2 v =

μ 0 μ

4 πr

3

cos λm

μ 0 μ

2 πr

3

sin λm

μ 0 μ

4 πr

3

cos^2 λm + 4 sin

2 λm =

μ 0 μ

4 πr

3

1 + 3 sin

2 λm ,

where cos

2 λm + sin

2 λm = 1 was used.

(b) We use Eq. 3-6:

tan φi =

Bv

Bh

(μ 0 μ/ 2 πr

3 ) sin λm

(μ 0 μ/ 4 πr

3 ) cos λm

= 2 tan λm.

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