The magnetic field induced by a current loop

In summary, a square loop of wire with a current of 10A flowing in the direction shown is centered at the origin and has four segments, each with a length of 10cm. We need to find the magnetic field at z=d on the z-axis. The solution provided by the professor involves finding the unit vectors a1 and a3, which can be calculated by dividing the x and z components of the position vector by the magnitude of the position vector. This allows us to find the angle between the position vector and the x and z axes, respectively. These unit vectors are then used to calculate the magnetic field at z=d using the Biot-Savart law.
  • #1
Engineering Student
2
0
A square loop of wire in the x-y plane, centred on the origin, is made up of four straight segments, each of length 2d=10cm. A current I =10A flows in the wire in the direction shown. Find the magnetic field at z=d on the z-axis.
(See "Diagram" for the diagram of the problem)
Here is the solution provided by the professor:
(See "solution1" for the solution of the problem)
I don't understand how he came up with the expression for unite vectors a1 and a3. Could some one explain this? Thanks.
Diagram.png
solution 1.png
 
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  • #2
Engineering Student said:
A square loop of wire in the x-y plane, centred on the origin, is made up of four straight segments, each of length 2d=10cm. A current I =10A flows in the wire in the direction shown. Find the magnetic field at z=d on the z-axis.
(See "Diagram" for the diagram of the problem)
Here is the solution provided by the professor:
(See "solution1" for the solution of the problem)
I don't understand how he came up with the expression for unite vectors a1 and a3. Could some one explain this? Thanks.
View attachment 99110 View attachment 99111
Welcome to the PF.

All I can see is a small attachment of the figure for the problem. Can you use the UPLOAD button to attach the figure and the solution to a reply? Thanks. :smile:
 
  • #3
Yes. I uploaded the pictures. You can get the pictures by clicking on the thumbnails.
 
  • #4
Engineering Student said:
Yes. I uploaded the pictures. You can get the pictures by clicking on the thumbnails.
I saw the pictures but feel belabored by your handwriting - I suggest typing in your solution. You can get all sorts of symbols by clicking on "Σ" in the toolbar above.
 
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1. What is a current loop?

A current loop refers to a closed path of electric current, where the current flows in one direction along the loop and returns in the opposite direction.

2. How is the magnetic field induced by a current loop?

The magnetic field induced by a current loop is caused by the movement of charged particles, such as electrons, within the loop. As these charged particles move, they create a magnetic field around the loop.

3. What factors affect the strength of the magnetic field induced by a current loop?

The strength of the magnetic field induced by a current loop is affected by the magnitude of the current in the loop, the number of turns in the loop, and the radius of the loop.

4. How is the direction of the magnetic field determined in a current loop?

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

5. What are some real-world applications of the magnetic field induced by a current loop?

The magnetic field induced by a current loop has various applications, including in electric motors, generators, and MRI machines. It is also used in magnetic compasses and particle accelerators.

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