(a) A proton, traveling with a velocity of 4.5 ×10^6 m / s due east, experiences a magnetic forc

step 1 All right, let's start with writing down everything that we know. We know the velocity, B, is 4

(a) A proton, traveling with a velocity of 4.5 ×10^6 m / s...

Key Concepts

Magnetic Force on a Moving Charge

This concept involves the force experienced by a charged particle moving in a magnetic field. The force is given by the equation F = |q| v B sin(?), where |q| is the magnitude of the charge, v is the speed of the particle, B is the strength of the magnetic field, and ? is the angle between the velocity and the magnetic field. When the force is maximum, sin(?) is 1, meaning the velocity and magnetic field are perpendicular.

Lorentz Force Equation

The Lorentz force equation defines the force on a charged particle moving in electric and magnetic fields. For a magnetic field, the relevant part of the equation is F = q(v × B), which shows that the force is a vector perpendicular to both the velocity and the magnetic field. This concept is critical for understanding how the direction and magnitude of the force depend on the particle's charge and its velocity relative to the magnetic field.

Right-Hand Rule and Sign of Charge

The direction of the force on a moving charge in a magnetic field is determined by the right-hand rule when the charge is positive. For a negative charge, such as an electron, the force direction is opposite to what is predicted by the right-hand rule. This concept helps in determining the orientation of the magnetic field when the force direction is known.

Magnetic Field Calculation

In problems involving the magnetic force on charges, determining the magnetic field’s magnitude often involves rearranging the magnetic force equation to solve for B. When the force and other parameters are known, and the velocity is perpendicular to the field, the field magnitude is found by B = F/(|q|v). This approach is fundamental in solving for the magnetic field in various electromagnetism problems.

Transcript

00:02 All right, let's start with writing down everything that we know.

00:06 We know the velocity, b, is 4 .5 times 10 to the 6th, and that's in meters per second.

00:33 We are given the force produced by the magnetic field, so i'll abbreviate that.

00:42 F subb, that is equal to 8 .0 times 10 to the minus 14th.

01:07 Now our force, as usual, is in newton's.

01:11 So, we're given that this is a traveling proton going at the speed.

01:19 So another thing we'll want to note is the charge of a proton.

01:33 It is 1 .6 times 10 to the minus 19th power.

01:43 And that is in coolness, unit of charge.

01:47 It is the charge of a proton.

01:49 So electrons and protons share the same charge.

01:53 Point of note electrons are just oppositely directed, oppositely charged.

02:01 Now the equation we're going to want to use to find the magnetic field is given by b is equal to f divided by the charge multiplied by the sign of the angle between the velocity and the force.

02:38 Theta.

02:40 We are given in this problem that the velocity is traveling east, and the force is directed south.

02:52 So let's write that out.

02:53 So we have our velocity.

03:01 And our force.

03:04 These are 90 degrees to each other.

03:07 So we have sign of 90 degrees or sign of pi over two, which is equal to 1.

03:12 So we don't need to keep that in this equation.

03:17 Now, this is a straight -up plug and chug.

03:22 We have everything we need to calculate it, but we need to find out the direction.

03:27 So you can find this from using the right -hand rule.

03:31 If you hold your right hand palm upwards out in front of you, points your thumb out to the side, point your pointer finger directly forward, and then your middle finger will point up in the direction your palm is facing.

03:43 It should all be at right angles to each other, all perpendicular.

03:47 So your pointer finger is the direction of the b field.

03:50 Your thumb is in the direction of the velocity, and your middle finger will be the force.

03:57 So if we orientate our right hand in the direction, we're given, so we have velocity to the east or to the right, and then we have the force is south...

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