Calculating Magnetic Moment of Rotating Spherical Shell

In summary, the formula for calculating the magnetic moment of a rotating spherical shell is μ = Iω, where μ is the magnetic moment, I is the moment of inertia, and ω is the angular velocity. The moment of inertia of a spherical shell can be calculated using the formula I = 2/3 * mr², where m is the mass of the shell and r is the radius. Angular velocity plays a crucial role in determining the magnetic moment, with a higher angular velocity resulting in a larger magnetic moment. The magnetic moment of a rotating spherical shell can be negative, indicating an opposite orientation to the angular velocity. This magnetic moment also affects the behavior of the shell in a magnetic field, with a larger moment resulting in a stronger
  • #1
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1. A spherical shell of radius R has a constant surface charge density, sigma. It rotates about its diameter with angular speed, w. Find the magnitude of the magnetic moment of the rotating spherical shell.


2. Magnetic dipole moment u = NIA(normal vector) ; Torque = u X B; Spherical Volume = 4/3 pi R^3


3. No idea where to start...
 
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  • #2
Consider an element of charge dq = σdA on the surface. As it spins around it becomes a current dI. Find the magnetic moment dm generated by this current then add all such magnetic moments over the surface of the sphere.
 

Related to Calculating Magnetic Moment of Rotating Spherical Shell

1. What is the formula for calculating the magnetic moment of a rotating spherical shell?

The formula for calculating the magnetic moment of a rotating spherical shell is μ = Iω, where μ is the magnetic moment, I is the moment of inertia, and ω is the angular velocity.

2. How is the moment of inertia of a spherical shell calculated?

The moment of inertia of a spherical shell can be calculated using the formula I = 2/3 * mr², where m is the mass of the shell and r is the radius.

3. What is the role of angular velocity in calculating the magnetic moment?

Angular velocity plays a crucial role in calculating the magnetic moment as it determines the rate at which the spherical shell is rotating. A higher angular velocity will result in a larger magnetic moment.

4. Can the magnetic moment of a rotating spherical shell be negative?

Yes, the magnetic moment of a rotating spherical shell can be negative. This indicates that the magnetic dipole moment is oriented in the opposite direction of the angular velocity.

5. How does the magnetic moment of a rotating spherical shell affect its behavior in a magnetic field?

The magnetic moment of a rotating spherical shell determines the strength of its interaction with a magnetic field. A larger magnetic moment will result in a stronger interaction with the magnetic field, while a smaller magnetic moment will result in a weaker interaction.

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