Magnetic dipole moment

In summary, to calculate the magnetic moment of the loop, we use the formula u = NIA, where N is the number of loops, I is the current, and A is the total area of the loop which is the sum of the area of the semicircle and rectangle. The correct answer is approximately 2.5 x 10^-4.
  • #1
jonathng
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0

Homework Statement



A wire is bent into the shape shown in the figure. The semi-circular part has a radius r = 4.00 cm and the rectangular part has a width w = 1.00 cm. A current of 0.300 A runs through the loop. What is the magnitude of the magnetic moment of the loop?

Note: The figure shows a semicircle with a small rectangle at the bottom. Making the rectangle 1cm by 8cm.

Homework Equations



u=NIA
Area of a circle
A=lw

The Attempt at a Solution



I have plugged in the values given and added the area of a rectangle to half the area of the circle, and I used one for the amount of loops.
So u=(1)(0.300)((.04^2 pi x0.5)+(.01x.08)

The answer I am getting is 9.9398e-4 which is incorrect. Any help is appreciated! Thanks!

 
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  • #2


Thank you for your question. There seems to be a small error in your calculation. The formula for the magnetic moment of a loop is u = NIA, where N is the number of loops, I is the current, and A is the area of the loop.

In this case, we have one loop, so N = 1. The current is given as 0.300 A. Now, for the area, we need to calculate the total area of the loop, which is the sum of the area of the semicircle and rectangle. The area of a semicircle is 1/2πr^2, so in this case it would be 1/2π(0.04 m)^2 = 0.00002513 m^2. The area of the rectangle is given as 0.01 m x 0.08 m = 0.0008 m^2. Therefore, the total area is A = 0.00002513 m^2 + 0.0008 m^2 = 0.00082513 m^2.

Plugging in these values into the formula, we get u = (1)(0.300)(0.00082513) = 0.000247539, or approximately 2.5 x 10^-4. I hope this helps! Please let me know if you have any further questions.
 

1. What is magnetic dipole moment?

Magnetic dipole moment refers to a measure of the strength of a magnetic field created by a magnet or a current-carrying loop. It is a vector quantity that has both magnitude and direction.

2. How is magnetic dipole moment calculated?

The magnetic dipole moment is calculated by multiplying the strength of the magnetic field by the area of the loop or the length of the magnet and the angle between the field and the loop or magnet. This can be represented by the equation M = B x A x cosθ, where M is the magnetic dipole moment, B is the magnetic field strength, A is the area of the loop or the length of the magnet, and θ is the angle between the field and the loop or magnet.

3. What is the unit of measurement for magnetic dipole moment?

The unit of measurement for magnetic dipole moment is ampere meter squared (A·m²) in SI units, or joule per tesla (J/T) in the cgs system.

4. What is the significance of magnetic dipole moment?

Magnetic dipole moment is an important concept in electromagnetism and is used to describe the behavior and interactions of magnets and electric currents. It is also used in various applications such as in magnetic resonance imaging (MRI) and in determining the magnetic properties of materials.

5. How does magnetic dipole moment relate to the Earth's magnetic field?

The Earth's magnetic field is believed to be generated by the motion of molten iron in its core. This creates a dipole moment that can be represented by a magnetic field with a north and south pole. The Earth's magnetic dipole moment is constantly changing and is responsible for phenomena like the aurora borealis.

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