The magnitude of Earth's magnetic field is about 0.5 gauss...

Name: Problem 18, Chapter 26: Essential University Physics
Uploaded: 2020-06-02T14:39:33-08:00
Duration: 4 min 23 s
Channel: Aspen Fenzl
Description: The magnitude of Earth's magnetic field is about 0.5 gauss near Earth's surface. What's the maximum possible magnetic force on an electron with kinetic energy of 1 keV? Compare with the gravitational force on the electron.

The magnitude of Earth's magnetic field is about 0.5 gauss near Earth's surface. What's the maximum possible magnetic force on an electron with kinetic energy of 1 keV? Compare with the gravitational force on the electron.

Key Concepts

Gravitational Force

This is the force exerted by gravity on a mass, calculated by F = mg. Comparing the gravitational force on an electron to the magnetic force offers insight into the relative strengths of these fundamental interactions.

Magnetic Field in Electromagnetism

Magnetic fields are vector fields that affect moving charges, and their strength—often measured in units like tesla or gauss—is a key parameter in quantifying the magnetic force exerted on a charge.

Lorentz Force

This is the fundamental force experienced by a charged particle moving through a magnetic field, described by the equation F = qvB sin(?). It is central to understanding how magnetic fields interact with moving electrons to produce force.

Kinetic Energy and Velocity Relationship

The relationship KE = 1/2 m v² allows us to derive a particle's velocity from its kinetic energy. This conversion is crucial when determining the magnitude of the force on a charged particle using the Lorentz force formula.

Transcript

00:01 In this example, we are trying to find the maximum magnetic force on an electron moving near the earth's surface.

00:07 So we've got a magnetic field of about 0 .5 ghosts, and we are given a kinetic energy of one kilo -electron volt.

00:15 So we can first write out the equation for the magnetic force, fb.

00:23 And if we assume that, well, first we can write equal to qb cross b.

00:31 But if the electron's moving really close to the earth, it'll be pretty much perpendicular, so the cross product can go away, and this will just become qvb.

00:42 And then we are given a kinetic energy of one kilo -electron volt, which, if you change that into joules, that is approximately 1 .6 times 10 to the minus 16 joules.

01:09 And we know another form of kinetic energy.

01:13 Well, okay, so if we're looking at the magnetic field, we notice that the first thing we need to find to get this for us is we have q and we have b, but we still need to find b.

01:24 So we're given this kinetic energy, and we can set this equal to 1 .5 mv squared, which is a form of kinetic energy.

01:37 And from this, we can find the velocity and put that into the magnetic field force equation.

01:43 So we put, you have the kinetic energy equal to this.

01:52 And if we rearrange this in terms of v, we get b is equal to square root of 2 times kinetic energy, 1 .6 times 10 to minus 16.

02:09 And this divided by the mass of the electron, which is 9 .11 times 10 to minus 31 kilograms.

02:21 We take that square root, we get a velocity equal to 1 .9 times 10 to the 7 meters per second...

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