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.
 

FAQ: Calculating Magnetic Moment of Rotating Spherical Shell

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.

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.

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.

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.

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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