# Homework Help: Magnetic Field of a quarter circle loop of charge

1. Feb 18, 2009

### Gogsey

Finfd the magnetic field at point p for the steady state configuration.

Ok so the picture is a quarter circle, with inner radius a and outer radius b, and point p is at the centre as if this was a full circle. The current is running around this loop.Picture the loop at the as going along the inner surface in one direction, the outer surface in the other direction, and going from a to b and from b to a.

Ok, I know how to evaluate this for the current enclosed by the loop. We just prove Ampere's Law in integral form, but I'm not sure what to do fo the magnetic field at point p, and even what it has to do with point p.

So theta is 90 degrees for both sides. fo both the top and bottom peice should be Mu(o)I/4.
Now the distance away for one is a and for the other is b.

So one should be Mu(o)Ia/4 and the other should be Mu(o)Ib/4

Then the magnetic field should be (Mu(o)I(a+b))/4

Does this even make sense? Sorry I can't post the pic but its not that hard to picture.
Mu(o) is supposed to be "mu naught".

2. Feb 18, 2009

### gabbagabbahey

The point P is the location that you want to calculate the field strength and direction at. The field varies as a function of position; 2cm away from a wire, there may be a very large field; while 100 miles away the field is probably very small. On on side of a wire, the field may point inward; on the other side it may point outward. The field will have a specific magnitude and direction at each different point. You want to find what the magnitude and direction is at the point P.

No, it makes absolutely no sense whatsoever. (Mu(o)I(a+b))/4 doesn't even have units of Teslas (or gauss).

Is this problem taken from a textbook? (Perhaps Griffiths Introduction to Electrodynamics prob. 5.9a)

You need to consider not only the magnitude of the fields of each segment of wire, but also their directions. Do the fields of the two curved sections point in the same direction, or in opposite directions (at P)? (Use the right hand rule!)

Do the straight line segments of the wire produce a magnetic field at the point P? Why not?

Also, the magnitude of the field produced by a single quarter-circular arc of radius R at the center is not $$\frac{\mu_0 I R}{4}$$....Its not even $$\frac{\mu_0 I}{4R}$$....start by looking up the correct formula for the field produced at the center of a whole circle of wire.....isn't the field do to a quarter circle (1/4)th of that?

Last edited: Feb 19, 2009
3. Feb 19, 2009

### Gogsey

Yes, I was completely on the wrong track. Yes the 2 edges of the quarter circle are both:

Ipi/2cr and one for r=a and r=b and one will be negative since the current runs in opposite directions for each quarter circle.