Understanding the Use of Magnetic Field in MIT Problem 4 31-9

[flyingpig]

Explain this MIT problem??

Homework Statement

http://web.mit.edu/course/8/8.02-esg/Spring03/www/8.02pset9sol.pdf

Problem 4 31-9

Why are they using x for the B-field? Isn't the distance from the rod to the loop h + w?? I don't understand on step 4.2

 

[cupid.callin]

what is h?

can you tell me via some image?

 

[SammyS]

They are integrating the B field over the area inside the loop. (Since I don't have the figure, I must go by the mathematics in their solution.) The loop must be distance, h, from the current carrying wire. The loop extends a distance, w, in the x direction and a distance L in the y direction.

 

[flyingpig]

Hm you are right, let me get the picture.

 

[flyingpig]

http://img96.imageshack.us/img96/6408/88948072.th.png

Uploaded with ImageShack.us

 

[flyingpig]

What do you mean "x direction"?

When I first did it I did this

$$\Phi = B \cdot A = \frac{\mu_0 I}{2\pi (h + w)} \cdot Lw$$

 

[ideasrule]

What do you mean "x direction"?

When I first did it I did this

$$\Phi = B \cdot A = \frac{\mu_0 I}{2\pi (h + w)} \cdot Lw$$

The magnetic field you used only applies at the very bottom of the loop. In general, B is given by mu_0*I/(2*pi*r), where r is the distance from the wire. You have to integrate over the area of the loop to get the flux.