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Chapter 28: Q 8P (page 829)

Question: An electric field of1.50kV/mand a perpendicular magnetic field of 0.400Tact on a moving electron to produce no net force. What is the electron’s speed?

Short Answer

Expert verified

The electron’s speed is |v|=3.75x103m/s.

Step by step solution

01

Given

ϕ=90.0∘E=1.50kVm=1.50x103V/mB=0.400TF=0

02

Determining the concept

Find the velocity of an electron by inserting the given values in the formula for electromagnetic force.

Formulae are as follow:

F=eE+evBsinϕ

Where, F is force, v is velocity, E is electric field, B is magnetic field, e is charge of particle.

03

Determining the speed of electron

The electromagnetic force experienced by an electron is,

F=eE+evBsinϕ

Inserting given values,

0=-1.6×10-19×1.50×103+-1.6×10-19×v×0.400×sin90∘0=-1.6×10-19×1.50×103-1.6×10-19×v×0.400×sin90∘v=1.50×1030.400v=3.75×103m/s

Hence, the electron’s speed is v=3.75×103m/s.

Therefore, the velocity of an electron can be determined by inserting the given values in the formula for electromagnetic force.

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Most popular questions from this chapter

Question: An electron has velocity v→=(32i^+40j^)km/s as it enters a uniform magnetic fieldB→=60i^ μT What are (a) the radius of the helical path taken by the electron and (b) the pitch of that path? (c) To an observer looking into the magnetic field region from the entrance point of the electron, does the electron spiral clockwise or counterclockwise as it moves?

Figure shows a wire ring of radiusa=1.8cmthat is perpendicular to the general direction of a radially symmetric, diverging magnetic field. The magnetic field at the ring is everywhere of the same magnitude B=3.4mT, and its direction at the ring everywhere makes an angle θ=20°with a normal to the plane of the ring. The twisted lead wires have no effect on the problem. Find the magnitude of the force the field exerts on the ring if the ring carries a current i=4.6mA.

An electron that has velocity ν→=(2.0×106m/s)i^+ (3.0×106m/s)moves through the uniform magnetic field B→= (0.030T)i^-(0.15T)j^.(a)Find the force on the electron due to the magnetic field. (b)Repeat your calculation for a proton having the same velocity.

Physicist S. A. Goudsmit devised a method for measuring the mass of heavy ions by timing their period of revolution in a known magnetic field. A singly charged ion of iodine makes 7revin a 45.0mTfield in 1.29ms. Calculate its mass in atomic mass units.

A proton, a deuteron (q=+e,m=2.0u), and an alpha particle (q=+2e,m=4.0u) all having the same kinetic energy enter a region of uniform magnetic field, moving perpendicular to it. What is the ratio of (a) the radius rd of the deuteron path to the radius rpof the proton path and (b) the radius rαof the alpha particle path to rp?
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