Crossed electric and magnetic fields are established over a certain region. The magnetic field i

Crossed electric and magnetic fields are established over a...

Key Concepts

Velocity Selector

A velocity selector utilizes crossed electric and magnetic fields to allow only particles with a specific speed to travel in a straight line while others are deflected. The condition for this is achieved when the electric force equals the magnetic force, which typically results in the equation v = E/B for particles where the net force is zero.

Lorentz Force

The Lorentz force is the force exerted on a charged particle by electromagnetic fields, and is given by the equation F = q(E + v x B). This principle is fundamental for understanding how a charged particle behaves in the presence of electric and magnetic fields.

Electric Force

The electric force is the force experienced by a charged particle when it is in an electric field, calculated using F = qE. It acts in the direction of the electric field for positive charges and opposite for negative charges, directly influencing the particle's acceleration.

Magnetic Force

The magnetic force on a charged particle moving through a magnetic field is given by F = q(v x B). This force acts perpendicular to both the velocity of the particle and the magnetic field, affecting the particle’s direction without changing its speed.

Crossed Electric and Magnetic Fields

In a crossed fields setup, electric and magnetic fields are oriented perpendicular to each other. This arrangement can be used to balance the electric and magnetic forces acting on a charged particle such that, at a specific velocity, the forces cancel each other, enabling the particle to move in a straight line.

Transcript

00:01 So in this question, we know that we have both electric field and magnetic field present.

00:06 The magnetic field has a magnitude of 0 .635 tesla, and the electric field has a magnitude of 2 .68 times 10 to the 6 volts per meter.

00:21 And the problem also tells us their direction.

00:25 In fact, their direction is such that they cross each other at a 90 degree.

00:30 Angle.

00:31 So for the magnetic field, the direction is vertically downward, and for the electric field, it is horizontally east, horizontally due east.

00:50 And then the problem tells us that we have an electron, and it travels in the direction of horizontally north.

01:07 So this is painting a 3d picture in my mind because think about a compass that is lying flat and how not only do you have the four directions on that plane, on that flat plane, you also have the direction of going up and down vertically crossing that plane.

01:27 Okay, so keep that in mind as we go further in this question.

01:31 And they tell us that this electron will go through both fields with zero net force.

01:41 And it will continue in a straight line.

01:43 And they're asking, okay, given all of these conditions, what must be its velocity? so before i do any more math with this problem, i want to draw a diagram.

01:55 So we have a better idea of how every factor plays in here.

02:00 So first, i will establish my directions.

02:05 So this is the compass i'm talking about.

02:07 You have north, south, west, east.

02:11 And i want you to just.

02:12 Think of this as a plane on its own and this plane is horizontal.

02:18 So imagine you are kind of laying this flat, then you should also have the direction that is into the page and out of the page.

02:30 If you're following the way i'm doing it, into the page will represent downward, vertically downward.

02:39 Okay, and out of the page will then represent vertically upward.

02:43 So, so what is happening right now is that we have electric field that is horizontally due east.

02:53 So the straight horizontal lines that i'm drawing in the east direction are the electric field lines.

03:02 And at the same time, you have the magnetic field vertically downward.

03:08 So based on our legend, downward means you're coming out of the page, or sorry, the page.

03:25 Okay, so here you have a crossed magnetic and electric fields.

03:30 And all the while, you have an electron moving vertically to, sorry, moving horizontally north...

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