Magnetic Field Current Loop

In summary, The problem involves a loop carrying current in the x-y plane and completing a circular arc from 60° to 360°, with horizontal and vertical sections. The objective is to find the magnitude of the magnetic field at point A, the center of the circular arc. The solution involves finding the field due to the vertical section of the loop using trigonometry and integrating the relevant equation. The horizontal section does not contribute to the field at the center.
  • #1
jromega3
27
0

Homework Statement



A loop carries current I = 2.5 A in the x-y plane as shown in the figure above. The loop is made in the shape of a circular arc of radius R = 4 cm from qo = 60 ° to q = 360 ° . The loop is completed by horizontal and vertical sections as shown.
What is BA, the magnitude of the magnetic field at point A, the center of the circular arc?

Homework Equations



For the loop part...
loopc3.gif


The Attempt at a Solution



Well, that's it if it were a complete loop, but this is 300/360, or 5/6 of a loop. So I take that and divide by 1.2 and I get 3.27e^-5.
Not sure about the other ones. My calculus is rusty at best.

It's hard to visualize maybe, but it's basically a circle from the 60 degree above the horizon all the way till the end, with a straight line going down to the horizontal center line and then a line connecting that line to the 0 degree mark on the curve.

As always, any help is appreciated.
 

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  • #2
Now you have to find the field due to the vertical section of the loop. By trig. you can see the length of the vertical section is 2sqrt3. The horizontal section does not produce any field at the centerIn the relevant equation take the integration of dx*sintheta/r^2 where dx is a small element of the straight vertical conductor, r is the distance of the element dx from the center and theta is the angle between the conductor and r.
 
  • #3


I would approach this problem by first using the Biot-Savart Law to calculate the magnetic field at point A. This law states that the magnetic field at a point due to a current-carrying wire is directly proportional to the current, the length of the wire, and the sine of the angle between the wire and the line connecting the point to the wire. In this case, we have a current-carrying loop, so we can break it up into smaller segments and integrate to find the total magnetic field at point A.

Using this approach, we can calculate the magnetic field at point A due to each segment of the loop. The horizontal and vertical sections of the loop will contribute a constant magnetic field, while the curved section will contribute a varying magnetic field. From there, we can use vector addition to find the total magnetic field at point A.

Without knowing the specific values for the radius and angle measurements, it is difficult for me to provide a numerical solution. However, I would recommend using this approach to calculate the magnetic field at point A. Additionally, it may be helpful to review the basics of vector calculus and integration to ensure a thorough understanding of the Biot-Savart Law and its application in this problem.
 

What is a magnetic field current loop?

A magnetic field current loop is a closed path of electrical current that creates a circular magnetic field around it.

What is the direction of the magnetic field in a current loop?

The direction of the magnetic field in a current loop is determined by the right-hand rule, which states that if you point your right thumb in the direction of current flow, the direction of your curled fingers will indicate the direction of the magnetic field.

How does the shape of the current loop affect the strength of the magnetic field?

The strength of the magnetic field in a current loop is directly proportional to the number of turns in the loop and the amount of current flowing through it. The more turns or the higher the current, the stronger the magnetic field will be.

What is the relationship between the magnetic field and the distance from the current loop?

The strength of the magnetic field decreases as the distance from the current loop increases. This relationship follows an inverse square law, where doubling the distance from the loop results in a quarter of the original magnetic field strength.

How is the magnetic field of a current loop used in applications?

The magnetic field of a current loop has many applications, including in electric motors, generators, and particle accelerators. It is also used in scientific research to study the behavior of charged particles in magnetic fields.

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