q1s - Physics 2212 K Quiz #1 Solutions Summer 2009 ²...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Physics 2212 K Quiz #1 Solutions Summer 2009 ² Permittivity constant m p Mass of a proton μ Permeability constant m e Mass of an electron e Fundamental charge c Speed of light K Coulomb constant g Acceleration due to gravity Unless otherwise directed, friction, drag, and gravity should be neglected, and all batteries and wires are ideal. Any integrals in free-response problems must be evaluated. I . (20 points) Two identical particles, each with mass m and positive charge q , are attached by ideal cords to the same point on an infinite uniform horizontal plane of positive charge, as illustrated. The plane causes a uniform electric field with magnitude E . When the particles are at equilibrium, there is an angle θ between their cords. What is the length, L , of the cords? Express your answer in terms of parameters defined in the problem, and physical or mathematical constants. ( On Earth, do NOT neglect gravity! ) . . . . . . . . . . . . . . Use Newton’s Second Law. Sketch a Free-Body Diagram. The forces on one of the particles are a weight mg , a tension T , an electric force due to the charged plane qE , and an electric force due to the other particle Kq 2 /r 2 . Note that r = 2 L sin θ 2 . Choose a coordinate system. Write out Newton’s Second Law in terms of magnitudes for each dimension. X F x = Kq 2 r 2- T x = ma x = 0 ⇒ T sin θ 2 = Kq 2 4 L 2 sin 2 θ 2 and X F y = qE- mg- T y = ma y = 0 ⇒ T cos θ 2 = qE- mg There are two unknowns, L and T . Since L is the answer to the question, eliminate T . One way is to divide the expression found from the x component of the forces by that found from the y component. T sin θ 2 T cos θ 2 = sin θ 2 cos θ 2 = Kq 2 4 L 2 sin 2 θ 2 qE- mg Solve for L . L 2 = Kq 2 cos θ 2 4( qE- mg )sin 3 θ 2 ⇒ L = s Kq 2 cos θ 2 4( qE- mg )sin 3 θ 2 Quiz #1 Solutions Page 1 of 4 1. (10 points) An electron orbits a fixed uniformly charged sphere. The orbital radius is R , and the speed of...
View Full Document

This note was uploaded on 05/08/2010 for the course PHYS 2212 taught by Professor Kindermann during the Summer '09 term at Georgia Tech.

Page1 / 4

q1s - Physics 2212 K Quiz #1 Solutions Summer 2009 ²...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online