sp97em_sol

# sp97em_sol - PHY6938 Proficiency Exam Spring 1997 February...

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Unformatted text preview: PHY6938 Proficiency Exam Spring 1997 February 25, 1997 E & M 1. Two small spheres of mass m are suspended from a common point by threads of length L . When each sphere carries a charge q , each thread makes an angle θ with the vertical as shown in the figure. Find an expression for the charge q at equilibrium in terms of L , m , g , θ , and the Coulomb constant k . m m q q L L θ θ The spheres are in equilibrium, this means that the total force affecting these two spheres is equal zero. To solve the problem we draw free body diagram for one of the spheres. F c F c mg T T = Tension in the string = Coulom force X Y θ Write equations of motion for one of the spheres. Using figure above we obtain m ¨ x = F c- T sin ( θ ) = kq 2 r 2- T sin ( θ ) = { r = 2 Lsin ( θ ) } = kq 2 (2 Lsin ( θ )) 2- T sin ( θ ) = (1) and m ¨ y = T cos ( θ )- mg = . (2) From Eq.1 and 2 we obtain T sin ( θ ) = kq 2 (2 Lsin ( θ )) 2 T = kq 2 (2 Lsin ( θ )) 2 sin ( θ ) (3) T cos ( θ ) = mg T = mg cos ( θ ) . (4) From Eq.3 and 4 we get kq 2 (2 Lsin ( θ )) 2 sin ( θ ) = mg cos ( θ ) q 2 = (2 Lsin ( θ )) 2 mgsin ( θ ) kcos ( θ ) . q = ± 2 Lsin ( θ ) s mg kcos ( θ ) . (5) Note, here sin ( θ ) and cos ( θ ) are always positive, since θ ≤ 90. 2. After improvements in magnet technology reduce the cost, physicists propose building a circular accelerator around the Earth’s circumference using bending magnets that provide a magnetic field of 2 T.using bending magnets that provide a magnetic field of 2 T....
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## This note was uploaded on 03/11/2012 for the course PHY 3900 taught by Professor Staff during the Fall '1 term at FSU.

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sp97em_sol - PHY6938 Proficiency Exam Spring 1997 February...

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