How Is Magnetic Induction Calculated in a Triangle of Parallel Wires?

In summary, the problem involves three parallel wires placed in the angles of an equilateral triangle with sides of 14 cm. The currents in the wires are 10A, 10A, and 20A, with the first and third currents flowing in opposite directions. The task is to find the magnetic induction at the center of the triangle. Using the formula B=I*μ0/2*pi*d, calculations show that the magnetic induction in the center is 5.1*10^-5 T, assuming all currents are in the same direction. However, if the third current is in the opposite direction, the magnetic induction would be 7.423*10^-5 T.
  • #1
zade70
61
0

Homework Statement


Three parallel wires are put in the angles of an equilateral triangle with sides 14 cm. The values of the currents are 10A,10A, 20A and the first and third are in different directions. Find the magnetic induction in the center of the triangle

Homework Equations


B=I*μ0/2*pi*d

The Attempt at a Solution


B1=B2=2.5*10^-5T
B3=5*10^-5T. I don't know which of these cases should I consider based on the problem's information.
Could you tell me which is right so I can continue with the sketch of induction?
http://postimg.org/image/4aco9wajl/
 
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  • #2
Doesn't matter:smile: for the magnitude. Do all four if you don't believe me,,,,,
 
  • #3
BvU said:
Doesn't matter:smile: for the magnitude. Do all four if you don't believe me,,,,,
So here's what I did. http://postimg.org/image/8licrhc1f/
B12=2.5*10^-5T (as the angle is 120 degress), B3=5*10^-5 T. As they are opposite vectors. (5-2.5)*10^-5=2.5*10^-5 T.
 
  • #4
Check the direction of B3.

Reason for this suspicion: I what would be the situation if all three currents were in the same direction and of equal magnitude ?
 
  • #5
BvU said:
Check the direction of B3.

Reason for this suspicion: I what would be the situation if all three currents were in the same direction and of equal magnitude ?
http://postimg.org/image/npe8682kp/
I corrected it.
The formula:
B=I*μ0/2*pi*d
B1=B2=2.4743*10^-5 T
B3=4.9486*10^-5 T
B=B12+B3=7.423 -10^-5 T, but the solution is 5.1*10^-5 T.
 

Related to How Is Magnetic Induction Calculated in a Triangle of Parallel Wires?

1. How is magnetic induction measured?

Magnetic induction is measured using a device called a magnetometer. The most commonly used magnetometer is a Hall effect sensor, which measures the strength of the magnetic field at a specific location.

2. What is the difference between magnetic induction and magnetic field?

Magnetic induction refers to the process of creating a magnetic field within a material, while magnetic field is the actual physical field that surrounds a magnet or a current-carrying wire. In other words, magnetic induction is the cause, while magnetic field is the effect.

3. How does the strength of the magnetic induction affect its properties?

The strength of the magnetic induction determines the level of magnetization and magnetic permeability of a material. Higher magnetic induction results in a stronger magnetic field and higher levels of magnetization, making the material more magnetic. It also affects the material's ability to conduct electricity and its response to external magnetic fields.

4. What factors can affect the magnetic induction of a material?

The magnetic induction of a material can be affected by its composition, temperature, and external magnetic fields. Different materials have different levels of magnetic susceptibility, which determines their response to magnetic fields. Temperature can also affect the alignment of magnetic domains within a material, altering its magnetic properties. External magnetic fields can also induce a magnetic field within a material and affect its magnetic induction.

5. How is magnetic induction used in everyday life?

Magnetic induction is used in a variety of everyday applications, such as generating electricity in power plants, creating magnetic storage in hard drives and credit cards, and in MRI machines for medical imaging. It is also used in a wide range of industrial and scientific processes, such as separating materials in recycling plants and measuring the Earth's magnetic field for navigation.

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