Name: Electricity & Magnetism (PHYS 196, CRN 30345) Spring 2016 Practice Final 2

Question

Name: Electricity & Magnetism (PHYS 196, CRN 30345) Spring 2016 Practice Final 2 1. A small toroidal solenoid consisting of Ni turns and turn-wrapping radius ri is nested inside a large toroidal solenoid of N2 turns and turn-wrapping radius rz such that the cores of both coils are centered on a circle of radius r. Both are air- core, but the nested coil is a continuous loop while the ends of the outer coil are connected to a battery of voltage va via a switch. If the resistance of the inner coil is Ri and the resistance of the outer coil is R2, find the magnitude of the current induced through the inner coil assuming the current through the outer coil increases linearly to its maximum in a time t. 2. Find the force exerted by a 5-mW laser beam striking a perfectly reflective, flat surface that is tilted thirty degrees from perpendicular to the beam. 3. A solid cylindrical copper wire of radius r carries a total current I straight out of the page, and the current is uniformly distributed throughout the wire's cross-section. At the very center of this wire is an infinitesimally fine, insulated wire carrying a current I in the opposite direction. Find the magnitude and direction (clockwise or counter-clockwise) of the magnetic field at a distance r/2 from the center of the solid wire, assuming the permeability there is 4. Find the power consumed by the central resistor 5. In the Hall Effect, current is forced to flow through a wide "slab" of conductive material lying in the plane of the page. The current flows up the page, but a strong magnetic field directed into or out of the page causes a detectable voltage to build up laterally in the slab. Suppose the current is 0.1 A and the magnetic field has a magnitude of 20 mT, but instead of being straight into the page, it is deflected 30° off alignment such that it is partially down the page. Find the voltage between the lateral sides of the slab if it is 2 mm x 2 mm square, and state which side is positive. Use-1.6x10-19 C for the electron charge.

Explanation / Answer

2.

Force = change in momentum /time = 2pcos30/t = 2Ecos30/ct = 2PCos30/c = 2 x 0.005 Cos30 / (3 x 108) = 2.886 x 10-11 N

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