A sphere of radius R carries a surface-charge distribution σ in the region of θ ∈ [π/2−α, π/2 +α], α is a fixed parameter. The rest of the sphere has no charge. The sphere is rotated about the z axis with constant angular velocity ω. (a) (20 pts) Find the magnetic dipole moment ~m. (b) (10 pts) Demonstrate that your solution is correct by considering two limits: α → π/2, α → 0. In the second limit assume that the total current is held fixed.

How many molecules are present in 3 mols of silicon dioxide (sio2)?

How have the competing explanations' experiments on atoms affected the development of the atomic model?

Asheet of steel 1.5 mm thick has nitrogen atmospheres on both sides at 1200oc and is permitted to achieve a steady-state diffusion condition. the diffusion coefficient for nitrogen in steel at this temperature is 6 x 10- 11 m2 /s, and the diffusion flux is found to be 1.2 x 10-7 kg/m2 -s. also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is 4 kg/m3 . how far into the sheet from this high-pressure side will the concentration be 2.0 kg/m3 ? assume a linear concentration profile.