# HW.9 - Electromagnetics Group.3 HW.9 Deadline 1 Find the...

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Electromagnetics HW.9 Group.3 Deadline 28 / 9 / 89 1. Find the magnetic field of the following steady currents: a) infinite uniform surface current ~ K = K 0 ˆ x flowing over the xy plane. b) two long coaxial solenoids each carry current I , but in opposite directions. The inner solenoids with radius a has n 1 turns per unit length, and the outer one has n 2 . Find ~ B inside, between and outside the solenoids. 2. A spherical shell of of radius R carrying a uniform surface charge density σ , is set spinning at angular velocity . Find the vector potential it produces at an arbitrary point ~ r . Also show that the magnetic field inside the spherical shell is uniform. These formulas may help you: ~v = ~ r × ~ K = σ~v Z u R 2 + r 2 - 2 rRu du = - R 2 + r 2 + Rru 3 R 2 r 2 p R 2 + r 2 - 2 Rru + C 3. A semicircular wire carries a steady current I . Find the magnetic field at an arbitrary point P on the other semicircle. 4. The washer-shaped coil shown here has a thickness Δ that is much less than the inner radius b and outer radius a .

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