Potential Energy and Torque in a Magnetic Field

In summary: Expert SummarizerIn summary, we discussed the calculation of magnetic potential energy and magnetic torque for a current-carrying coil in a uniform magnetic field. For the potential energy, the equation used is U = -I (dot product) A (dot product) B, where I is the current, A is the area of the coil, and B is the magnetic field. When taking the dot product, the y component of B can be ignored since the coil is parallel to the xz plane. For the torque, the vector form of the dipole moment is <3u, 0, u>, and the calculation is T = -(3u, 0, u) (cross product) (2.20, -
  • #1
San1405
4
0

Homework Statement



The coil in the figure below carries a current of 2.00 A in the direction indicated, is parallel to an xz plane, has 3 turns, an area of 4.20 10-3 m2, and lies within a uniform magnetic field = (2.20 - 2.85 - 3.65 ) mT.

(a) What is the magnetic potential energy of the coil - magnetic field system?


(b) What is the magnetic torque on the coil?



Homework Equations



U = -u (dot product) B

T= -u (cross product) B

The Attempt at a Solution



So, in order to calculate the Potential Energy, I tried to take the magnitude of B and multiply it by the dipole moment. I got 1.29e-4. For some reason, this is not correct. I know I should not include one of the vectors of B. I tried not including the x and z vectors, but that didn't work. I also tried to not include the y vector, but that didn't work either. I have no idea what to do!
For the second part, I know how to take the cross product, but I do not know what the vector form of u is. I know the y vector is 0, but how do I find the x and z vector? i tried simply using <u,0,u>, but that didn't work.
Thank you for your time!
~San
 
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  • #2
jay

Hello Sanjay,

Thank you for your post. For the magnetic potential energy of the coil - magnetic field system, it looks like you are on the right track. However, there are a few things to keep in mind.

Firstly, the magnetic potential energy equation you have written is for a magnetic dipole, not a current-carrying coil. In this case, you will need to use the equation U = -I (dot product) A (dot product) B, where I is the current, A is the area of the coil, and B is the magnetic field.

Secondly, when taking the dot product, you do not need to include the y component of the magnetic field, as the coil is parallel to the xz plane. So the calculation would be U = -(2.00 A) (4.20 x 10^-3 m^2) (2.20 mT) = -1.85 x 10^-5 J.

For the magnetic torque on the coil, you are correct in using the cross product. In this case, the vector form of the dipole moment would be <3u, 0, u>, where u is the magnitude of the dipole moment. Then, T = -(3u, 0, u) (cross product) (2.20, -2.85, -3.65) mT = (-3u, -3.65u, 2u) mT.

Hope this helps! Let me know if you have any further questions.


 

1. What is potential energy in a magnetic field?

Potential energy in a magnetic field refers to the energy that a charged particle possesses due to its position in a magnetic field. This energy is a result of the interaction between the charged particle and the magnetic field.

2. How is potential energy calculated in a magnetic field?

The formula for calculating potential energy in a magnetic field is PE = qVB, where q is the charge of the particle, V is the velocity of the particle, and B is the strength of the magnetic field. This formula is based on the work done by the magnetic force on the charged particle.

3. What is the relationship between potential energy and torque in a magnetic field?

Potential energy and torque are closely related in a magnetic field. Torque is defined as the force that causes an object to rotate around an axis, and this force is directly proportional to the potential energy of the charged particle in the magnetic field.

4. Can potential energy be converted into kinetic energy in a magnetic field?

Yes, potential energy can be converted into kinetic energy in a magnetic field. As a charged particle moves in a magnetic field, its potential energy decreases and its kinetic energy increases. This conversion is a result of the work done by the magnetic force on the charged particle.

5. How does the direction of the magnetic field affect potential energy and torque?

The direction of the magnetic field plays a crucial role in determining the potential energy and torque in a magnetic field. The magnitude of potential energy and torque can change depending on the direction of the magnetic field, as well as the direction of the motion of the charged particle within the field.

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