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(a) What is the speed of a beam of electrons when the simultaneous influence of an electric field of $1.56 \times 10^{4} \mathrm{V} / \mathrm{m}$ and a magnetic field of $4.62 \times 10^{-3} \mathrm{T}$ , with both fields normal to the beam and to each other, produces no deflection of the electrons? (b) In a diagram, show the relative orientation of the vectors $\vec{\boldsymbol{v}}$ , $\vec{\boldsymbol{E}}$ and $\vec{\boldsymbol{B}}$ . (c) When the electric field is removed, what is the radius of the electron orbit? What is the period of the orbit?

a)V $=3.4 \times 10^{\wedge} 6 \mathrm{m} / \mathrm{s}$c) $\mathrm{R}=4.19 \times 10^{\mathrm{N}}$

Physics 101 Mechanics

Physics 102 Electricity and Magnetism

Chapter 20

Magnetic Field and Magnetic Force

Motion Along a Straight Line

Motion in 2d or 3d

Electric Charge and Electric Field

Gauss's Law

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Magnetic Field and Magnetic Forces

Sources of Magnetic field

Electromagnetic Induction

Inductance

Cornell University

University of Washington

McMaster University

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so here. If there's no deflection, this means that the velocity is simply going to be equal to the magnitude of the electric field divided by the magnitude of the magnetic field. Here we only have a magnetic force and there is a centripetal acceleration. So we can say that the magnetic force equals the mass times X s a triple acceleration. And so we can say that the absolute value of the charge times the velocity times at the magnitude of the magnetic field will equal the mass times the velocity squared, divided by the radius for party. They simply want the velocity. So this is going to be equal to the magnitude of the electric field divided by the magnitude of the magnetic field. This is going to be equal to 1.56 times 10 to the fourth. This will be volts per meter, and then this will be divided by 4.6 two times 10 to the negative third, Tesla's and this is giving us 3.38 times 10 to the sixth meters per second. So at this point part, ah bee, we can draw a diagram of what's going on. So in this negative y direction. We have the electric field in the negative X direction. We have the velocity and then going into the page, there's going to be the magnetic field. So for parts, whether this would be for part B, this would give you direction of all the factors for port. See, however, we want to find the radius. So we're simply taking this equation right here. And isolating are so are is going to be equal to ah Wien, divided by the absolute value of the charge times the magnitude of the magnetic field this is going to be equal Teo the mass of an electron, a 9.11 times 10 to the negative, 31st kilograms and then times the velocity that we just found. 3.38 times 10 to the sixth meters per second and then divided by the charge on election. So 1.6 times 10 to the negative 19th and then times the magnitude of the magnetic field 4.62 times 10 to the negative. Third, Tesla's and we find that the radius is going to be equal to 4.17 times 10. The negative third meters, so this would be your answer. Now, However, the other question two Part C is asking for the period. So we can say that the period is simply going to be equal to the circumference divided by the velocity. So we can say to pie are divided by V so we can say to pi times the are that we just found so 4.17 times 10 to the negative third meters and then divided by thieves velocity of 3.38 times 10 to the sixth meters per second. And so the period is going to be equal to 7.74 times 10 to the negative ninth seconds. So this would be the time per revolution. That is the end of the solution. Thank you for watching.

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