Magnetic Field of a quarter circle loop of charge

In summary, the conversation discusses finding the magnetic field at point P in a steady state configuration. The field varies as a function of position and has a specific magnitude and direction at each point. The formula used to calculate the field at the center of a whole circle of wire is needed, and the direction of the fields of each wire segment must be considered. The correct formula for the field produced by a quarter circle at the center is also mentioned.
  • #1
Gogsey
160
0
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 piece 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".
 
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  • #2
Gogsey said:
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.

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.
Gogsey said:
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".

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 [tex]\frac{\mu_0 I R}{4}[/tex]...Its not even [tex]\frac{\mu_0 I}{4R}[/tex]...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?:wink:
 
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  • #3
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.
 

Related to Magnetic Field of a quarter circle loop of charge

1. What is a quarter circle loop of charge?

A quarter circle loop of charge is a curved path formed by a charged particle that moves in a circular motion, covering one-fourth of the circle.

2. How is the magnetic field of a quarter circle loop of charge calculated?

The magnetic field of a quarter circle loop of charge can be calculated using the equation B = μ0I/4R, where μ0 is the permeability of free space, I is the current flowing through the loop, and R is the radius of the loop.

3. What direction does the magnetic field point in a quarter circle loop of charge?

The direction of the magnetic field in a quarter circle loop of charge is always perpendicular to the plane of the loop and follows the right-hand rule, with the direction of the field determined by the direction of the current flow.

4. How does the radius of the loop affect the magnetic field in a quarter circle loop of charge?

The magnetic field in a quarter circle loop of charge is directly proportional to the radius of the loop. As the radius increases, the magnetic field becomes stronger and vice versa.

5. What is the significance of the magnetic field in a quarter circle loop of charge?

The magnetic field in a quarter circle loop of charge is important in understanding the behavior of charged particles in circular motion and is also used in various applications such as electromagnets and electric motors.

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