This may seem familiar

Electricity and Magnetism Level 5

A positive point charge is at rest on the + y +y axis and is at a certain distance from the origin. The electric field is static, uniform, and directed towards the − y -y axis. The magnetic field is static, nonuniform, directed towards the − z -z axis, and set up such that if the charge is given a slight push towards the + x +x axis, the charge undergoes circular motion, with the origin as the center of curvature. Eventually, the charge arrives at certain points along the circular path, where the magnetic field is zero. Determine the angle between the + y +y axis and the position vector of the first such point that the point charge encounters.

Express your answer in degrees and round off to the nearest integer.


The answer is 48.

Ramon Vicente Marquez by Ramon Vicente Marquez , 26, Philippines

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1 solution

Evaluating the work done by the electric field from the initial point to the point of interest, and using work energy theorem:

q E R ( 1 − c o s x ) = 1 2 m v 2 q E R (1 - cos x) = \frac{1}{2} m v^2

Evaluating the Lorentz force at the point of interest, and using the centripetal component of Newton's 2nd Law in circular motion:

q E c o s x = m v 2 R q E cos x = \frac{m v^2}{R}

The two equations yield:

c o s x = 2 3 cos x = \frac{2}{3}

x = 4 8 o x = 48^o

Notice the similarity to problem 3 in this link:

http://ocw.mit.edu/courses/physics/8-012-physics-i-classical-mechanics-fall-2008/exams/exam2sol.pdf

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