Magnetic field and magnetic force between wires

In summary, the density of the magnetic field is equal to the Earth's magnetic field at a distance of 2.27 m from the wire, and the force on the wires between two supporting pillars is 1.65 N when the wires are spaced 5 m apart. It is important for scientists to always double check their calculations and assumptions to ensure accuracy.
  • #1
mmoadi
157
0

Homework Statement



Electricity from the power plant with a power P = 100MW is transmitted by V= 220kV line. At what distance from the wire is the density of the magnetic field equal to the density of the Earth's magnetic field B(earth) = 4 × 10^-5 T? What is the force on the L= 200 m long sections of wires between two supporting pillars, if the two wires are spaced d= 5 m?

Homework Equations



P= V*I
B= (μ(0)*I)/ (2πr)
F= I*L*B

The Attempt at a Solution



First part: At what distance from the wire is the density of the magnetic field equal to the density of the Earth's magnetic field BZ = 4 × 10^-5 T?

P= V*I → I= P/V
I= 100 MV/ 220 kV
I= 454.5 A

B= (μ(0)*I)/ (2πr) → r= (μ(0)*I)/ (2πB)
r= (4π x 10-7 N/A²*454.5 A)/ (2π*4 × 10^−5 T)
r= 2.27 m

Are my calculations correct?:confused:

Second part: What is the force on the 200 m long sections of wires between two supporting pillars, if the two wires are spaced 5 m?

F= I*L*B
F= I*L*((μ(0)*I)/ (2πd))
F= 1.65 N

Are my calculations correct?:confused:

Thank you for helping!:smile:
 
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  • #2
it is important to always check your calculations and make sure they are accurate. In this case, your calculations appear to be correct. However, it is always a good idea to double check your work and make sure you have used the correct units and values for the constants.

For the first part, you correctly used the formula for magnetic field strength and solved for the distance from the wire. Your final answer of 2.27 m is reasonable and aligns with the expected value for the Earth's magnetic field at that distance.

For the second part, you correctly used the formula for force and solved for the force on the wires. Your final answer of 1.65 N is also reasonable and aligns with the expected value for the force on the wires at that spacing.

Overall, your calculations appear to be correct and your reasoning is sound. Well done! it is important to always double check your work and make sure your calculations and assumptions are accurate. Keep up the good work!
 
  • #3


I would like to point out that your calculations seem to be correct based on the given information. However, I would like to clarify a few things for a better understanding.

1. When solving for the distance at which the magnetic field is equal to the Earth's magnetic field, you have used the formula for the magnetic field created by a straight wire. This is correct, but it only gives you the magnetic field at a specific point on the wire. To find the distance at which the magnetic field is equal to the Earth's magnetic field, you need to use the formula for the magnetic field created by a long straight wire, which is B = (μ(0)*I)/ (2πr). This will give you the average magnetic field along the entire length of the wire.

2. In the second part, when calculating the force on the wires, you have correctly used the formula F= I*L*B. However, the value of B that you have used is the magnetic field at a specific point on the wire. To find the average magnetic field along the entire length of the wire, you need to use the formula B = (μ(0)*I)/ (2πd). This will give you the average magnetic field between the two wires.

Overall, your calculations seem to be correct, but it is important to use the correct formulas to get accurate results. I hope this helps!
 

What is a magnetic field?

A magnetic field is a region in space where a magnet or a moving electric charge experiences a force. It is represented by lines of force that show the direction and strength of the magnetic force.

How is a magnetic field created?

A magnetic field is created by moving electric charges or by the presence of magnetic materials such as magnets. In the case of wires, a magnetic field is created when electric current flows through the wire.

What is the relationship between magnetic field and magnetic force?

The magnetic field exerts a force on moving electric charges, which is known as the magnetic force. The direction of this force is perpendicular to both the direction of the magnetic field and the direction of motion of the charges.

How do the magnetic fields of two parallel wires interact?

The magnetic fields of two parallel wires interact with each other and can either attract or repel depending on the direction of the current flow. If the currents are in the same direction, the wires will attract, and if they are in opposite directions, they will repel.

What factors affect the strength of the magnetic force between wires?

The strength of the magnetic force between wires is affected by the distance between the wires, the amount of current flowing through the wires, and the direction of the current flow. The force increases as the distance decreases and as the current increases.

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