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hw8 - Electricity and Magnetism I(P331 Homework 8 Due...

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Electricity and Magnetism I (P331) Homework 8 Due: Wednesday, November 11, 4:00 PM 1. Suppose that in a region of space the vector potential is given by A = k ˆ φ . What is the current density? 2. At the surface of the Earth, the magnetic field of the Earth is approximately the same as the field from a point dipole m E at the center of the Earth. The dipole moment is: m E = m E (sin θ 0 cos φ 0 ˆ x + sin θ 0 sin φ 0 ˆ y + cos θ 0 ˆ z ) , (1) where m E = 7 . 79 × 10 22 A · m 2 and ( θ 0 , φ 0 ) = (169 , 109 ). The z axis is the Earth’s rotation axis and the x axis passes through the Prime Meridian; positive φ is to the east. (a) Calculate the magnetic field B at a point on the Earth with colattitude θ and longitude φ . Give the components of B to the north ( - ˆ θ ), to the east ( ˆ φ ), and vertical (ˆ r ). (b) Compute these components for Bloomington in gauss. (1 gauss = 10 - 4 Tesla.) 3. A charged annulus with inner radius a , outer radius b , and surface charge density σ lies in the x, y -plane with its center at the origin. It rotates about the z
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