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- Homework Statement
- A sphere of radius r=5cm and volume charge density ρ=14μC/m^3

spins at ω=200rad/s. What is the magnetic field at the center of the sphere in Tesla? Hints: this requires a great deal of integration, and the resulting field is very small.

- Relevant Equations
- Magnetic field at a point on the center axis of a loop of current:

$$B = \frac{\mu_0 I}{2\pi(y +R^2)^{3/2}}\hat{j}$$

if a sphere rotates, it's like multiple currents going around in a circle. I can find the magnetic field of each of those currents at the center point of the circle and add them together. We can integrate with respect to y and R. y ranges from 0 to 5 cm away from the center of the loop and the radius also ranges from 0 to 5 cm. However, I'm not sure how to incorporate volume charge density into the equation. Do you guys have any ideas?