Magnetic fields due to currents help

In summary: If you point your thumb in the direction of the current, your fingers should curl around the wire in the direction of the magnetic field.In summary, the problem involves four long straight wires forming a square with a current of 19 A in each wire. The wires are labeled 1-4 and the currents are out of the page in wires 1 and 4, and into the page in wires 2 and 3. The question asks for the magnitude of the net magnetic field at the center of the square. The diagram in the solution is not to scale and the +1, -2, -3, and 4 labels do not match the original wires labeled 1-4. To determine the direction of the magnetic field
  • #1
Nyasha
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Homework Statement



In the figure 29-49, four long straight wires are perpendicular to the page, and their cross sections form a square of edge length a = 20 cm. The currents are out of the page in wires 1 and 4 and into the page in wires 2 and 3, and each wire carries 19 A. What is the magnitude of the net magnetic field at the square's center?


http://edugen.wiley.com/edugen/courses/crs1650/art/qb/qu/c29/fig29_45.gif




Solution


I don't understand how they got the diagram with the directions of b1,b2,b3 and b4

200710256626332888916287800006317.jpg
 
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  • #2
Nyasha said:
I don't understand how they got the diagram with the directions of b1,b2,b3 and b4

There are a couple of confusing things about the picture in the solution:

Firstly, Each vector seems to be going out on its own angle. This is not true, the drawing is not to scale. Treat both B2 and B4 having the same angle, and B1 and B3 having the same angle. I guess the artist is simply trying to make it clear that there are 4 separate vectors, even though two of them are identical, and another two of them are identical.

Secondly, Ignore the +1, -2, -3, and 4 in the corners of the square. I don't know what those are about. They don't match up with the original wires labeled 1, 2, 3, and 4 at all. So when you are trying to figure out which wire goes with which B, look at the figure in the problem statement to get the correct wire number.

If you adhere to the above, the directions fit with the right hand rule.
 

Related to Magnetic fields due to currents help

1. What is a magnetic field and how is it related to electric currents?

A magnetic field is a region in space where a magnetic force can be experienced. It is created by moving electric charges, such as the flow of electric current. The strength and direction of the magnetic field is determined by the magnitude and direction of the current.

2. How do magnetic fields due to currents help in everyday life?

Magnetic fields due to currents have several practical applications in everyday life. They are used in motors and generators to convert electrical energy into mechanical energy and vice versa. They are also used in magnetic resonance imaging (MRI) machines in healthcare, as well as in compasses for navigation.

3. What is the right-hand rule and how is it used to determine the direction of a magnetic field?

The right-hand rule is a mnemonic device used to determine the direction of a magnetic field around a current-carrying wire. It states that if you point your right thumb in the direction of the current, then the direction of the fingers curling around the wire represents the direction of the magnetic field lines.

4. How does the strength of a magnetic field due to a current change with distance?

The strength of a magnetic field due to a current decreases with distance from the current. This relationship follows an inverse square law, meaning that the strength of the magnetic field is inversely proportional to the square of the distance from the current.

5. Can magnetic fields due to currents be shielded or blocked?

Yes, magnetic fields due to currents can be shielded or blocked. This can be achieved by using materials with high magnetic permeability, such as iron or steel, which can redirect the magnetic field lines and reduce their strength. Additionally, distance from the source of the current can also reduce the strength of the magnetic field.

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