Magnetic Field at the center of a sphere magnet

In summary, the conversation discusses using the Biot-Savart equation to find the magnetic field at the center of a sphere magnet with uniform magnetization along the z-axis. There is a question about why the denominator in the equation uses R3=(a2+z2) instead of R3=(rloop2+z2) and a request to show that the effective current due to the magnetization is zero except at the surface of the sphere.
  • #1
hansbahia
55
0

Homework Statement


A sphere magnet of radius a has permanent uniform magnetization, z-axis. So we were trying to find the magnetic field at the center of the magnet in class.

Homework Equations


[itex]j_M(θ)=Msin(θ)[/itex]

[itex]dI=j_M(θ)adθ[/itex]

circular loop

[itex]r_{loop}=asin(θ)[/itex]

The Attempt at a Solution



When using Biot-Savart equation for magnetic field of a ring why do you use*
[itex]R^3=(a^2+z^2)[/itex]

instead of

[itex]R^3=(r_{loop}^2+z^2)[/itex]

for the denominator?
 
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  • #2
hansbahia said:
When using Biot-Savart equation for magnetic field of a ring why do you use*
[itex]R^3=(a^2+z^2)[/itex]

instead of

[itex]R^3=(r_{loop}^2+z^2)[/itex]

for the denominator?

Did you mean to write R2 instead of R3?

Can you show that the effective current due to the magnetization is zero everywhere except at the surface of the sphere?
 

What is the magnetic field at the center of a sphere magnet?

The magnetic field at the center of a sphere magnet is zero. This is because the magnetic field lines are symmetrical and cancel each other out at the center.

How does the magnetic field at the center of a sphere magnet vary with distance?

The magnetic field at the center of a sphere magnet does not vary with distance. It remains zero regardless of how far away you are from the magnet.

Can the magnetic field at the center of a sphere magnet be manipulated?

No, the magnetic field at the center of a sphere magnet cannot be manipulated. It is a fixed characteristic of the magnet and cannot be changed.

What factors affect the magnetic field at the center of a sphere magnet?

The magnetic field at the center of a sphere magnet is affected by the strength of the magnet, the size of the magnet, and the permeability of the material it is made of.

How can the magnetic field at the center of a sphere magnet be measured?

The magnetic field at the center of a sphere magnet can be measured using a magnetometer, a device that detects and measures magnetic fields.

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