A uniform magnetic ficld points north; its magnitude is 1.5...

A uniform magnetic ficld points north; its magnitude is 1.5 T. A proton with kinetic energy $8.0 \times 10^{-13} \mathrm{J}$ is moving vertically downward in this field. What is the magnetic force acting on it?

Key Concepts

Lorentz Force

The Lorentz force describes the force exerted on a moving charged particle in the presence of a magnetic field. It is given by the vector equation F = q(v × B), where q is the charge, v is the velocity of the particle, and B is the magnetic field. The magnitude of this force is determined by q, the speed of the particle, the strength of the magnetic field, and the sine of the angle between the velocity and magnetic field vectors. This concept is fundamental to understanding how charged particles behave in magnetic fields, including the resulting circular or helical paths when the velocity and field are not parallel.

Kinetic Energy and Velocity Relationship

The kinetic energy of an object is directly related to its mass and the square of its velocity, as given by the equation KE = (1/2)mv². This relationship allows one to compute the speed of a particle when its kinetic energy and mass are known. In problems involving magnetic forces on charged particles, determining the velocity from the kinetic energy is often a crucial step because the force depends linearly on the particle's speed.

Transcript

00:01 In this question, we know that the magnitude of the magnetic field is 1 .5 tesla, and the direction is pointing north.

00:09 So very similar to the previous two questions.

00:13 But instead of telling us of a charge that is moving at a certain speed, they give us the kinetic energy of the proton.

00:22 So the kinetic energy magnitude is 8 .0 times 10 to the negative 13th joules, and this is of a proton, and that is relevant.

00:33 And they tell us that this is vertically downward in the magnetic field.

00:44 So assuming that this is the same as the previous two questions, then your magnetic field is north, and so that is completely horizontal.

00:58 And if you have kinetic energy that is vertically downward, then again notice that your velocity will also be vertically downward.

01:08 And the relationship or the angle between the velocity vector and the magnetic field vector will once again be 90 degrees.

01:16 And sign of 90 degrees will just give you one.

01:20 So this will be relevant as we apply this angle into the formula for finding magnetic force.

01:27 And that is what they're looking for.

01:29 They're looking for what is the magnetic force exerted on this proton? well, before we get to magnetic force, by the way, we recognize that magnetic force magnitude is found by q times v crossed with b.

01:45 And of course, sign of 90s 1, so you can omit writing that.

01:49 But you have to notice that we don't have velocity in this question.

01:53 We have to figure it out from our given value for kinetic energy.

01:59 So that's what we're going to do first...

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