Magnetic fields/basics

1. Nov 2, 2005

I just need to know what I am doing wrong. Maybe there is a concept I don't get right. Please help.

Find the magnitude and direction of the magnetic field $$\vec{B}$$ at point P in Fig. 30-32, for i = 30 A and a = 8.0 cm.

FIG ATTACHED

My work:

I see that on the inner side, the magnetic field of all parts is "into." So the problem is finding the individual magnitudes and summing 'em up. Here is what I have

General procedure for finite wires:

$$B=\frac{\mu _0 I}{4\pi y} \frac{L}{\sqrt{x^2 + y^2}}$$

Sections
A:
$$y=\frac{a}{4}$$

$$x=\frac{a}{4}$$

$$L=x$$

DIR: $$\otimes$$

B:

$$y=\frac{a}{4}$$

$$x=\frac{a}{4}$$

$$L=x$$

DIR: $$\otimes$$

C:

$$y=\frac{a}{4}$$

$$x=\frac{3a}{4}$$

$$L=x$$

DIR: $$\otimes$$

D:

$$y=\frac{3a}{4}$$

$$x=\frac{a}{4}$$

$$L=x$$

DIR: $$\otimes$$

E:

$$y=\frac{3a}{4}$$

$$x=\frac{a}{4}$$

$$L=x$$

DIR: $$\otimes$$

F:

$$y=\frac{3a}{4}$$

$$x=\frac{3a}{4}$$

$$L=x$$

DIR: $$\otimes$$

G:

$$y=\frac{a}{4}$$

$$x=\frac{a}{4}$$

$$L=x$$

DIR: $$\otimes$$

Then, the final result is the following sum

$$B=\frac{\mu_0 I \left( 4\sqrt{5} + 7 \right) \sqrt{2}}{6a\pi} \approx 5.6372 \times 10^{-4} \mbox{ T}$$

DIR: $$\otimes$$

But, it's wrong!! I can't see why.

Problem #2.

Each of the eight conductors in Fig. 30-41 carries 3.4 A of current into or out of the page. Two paths are indicated for the line integral $$\oint \vec{B} \cdot d\vec{s}$$.

FIG ATTACHED

What is the value of the integral for the path at the left?

My work:

$$\oint \vec{B} \cdot d\vec{s} = \mu _o I_{enc} = \mu _o \left( I + I -I \right) = \mu _o I \approx 4.273 \times 10 ^{-6} \mbox{ T}\cdot \mbox{m}$$

ANY HELP IS HIGHLY APPRECIATED

Attached Files:

File size:
4.6 KB
Views:
53
• fig_8a.JPG
File size:
5.9 KB
Views:
48
Last edited: Nov 2, 2005