A wire having a mass per unit length of 0.500 g/cm carries a 2.00-A current horizontally to the

step 1 Alrighty, we've got a pretty interesting problem here. We've got a wire. It's got a mass per uni

A wire having a mass per unit length of 0.500 g/cm carries a...

Key Concepts

Right-Hand Rule for Determining Force Direction

The right-hand rule is used to determine the direction of the force on a current-carrying conductor immersed in a magnetic field. With the thumb pointing in the direction of the current and the index finger in the direction of the magnetic field, the middle finger then points in the direction of the resulting force. This tool is essential for correctly orienting the magnetic field to produce a force in a desired direction.

Lorentz Force on a Current-Carrying Conductor

This concept explains that a current-carrying wire placed in a magnetic field experiences a force given by F = I (L x B), where I is the current, L is the length vector (in the current's direction), and B is the magnetic field. The magnitude of the force per unit length is I·B when the current and field are perpendicular.

Equilibrium of Forces (Weight vs. Magnetic Force)

To lift the wire, the upward magnetic force must balance the downward gravitational force (weight) of the wire. The weight per unit length is given by ?g, where ? is the mass per unit length and g is the acceleration due to gravity. Setting I·B equal to ?g allows one to solve for the minimum magnetic field magnitude required for levitation.

Transcript

00:01 Alrighty, we've got a pretty interesting problem here.

00:02 We've got a wire.

00:02 It's got a mass per unit length of a half a gram per centimeter.

00:08 And there's also a current that's going through this wire, and it's going horizontally through it.

00:13 And they tell us it's going in the direction of the south.

00:17 And what we want to figure out is what is the direction and the magnitude of the minimum magnetic field needed so that the wire that we have will actually be able to, um, um, um, um, be able to like lift upward.

00:35 The minimum.

00:36 Remember, we're looking for the minimum.

00:39 So let's go give that a shot.

00:40 Let's give that a shot.

00:41 That should be pretty interesting.

00:45 First and foremost, we want to start with the right hand rule.

00:50 They ask for the direction first, so that's a good place to start here.

00:53 And i use the right hand rule, we got the direction.

00:56 So we know that the magnetic field must be in the positive x direction or east, the way they say it.

01:02 If the magnetic force is in the positive z direction, or the upward direction and the current is in the negative y direction or the south direction all right so let's go ahead and we'll write that answer here.

01:14 We know that the b field b field must be in the in the positive x direction so i want to go ahead and say it's i i had direction.

01:26 Okay and just to clarify this a little bit more i could sketch it for you guys just based on what we know we know that the magnetic force is in the positive z direction right so if you have some sort of wire here you're going to have a magnetic force in this direction and we have and that's in the positive z direction so we can say that's the positive g a direction and then you have a current in the negative y direction okay um negative y direction so if you would just imagine a chorded axis system like this, your current will be in this direction here.

02:07 I, like so.

02:09 And then if you use the right hand rule, you can figure out which direction your b field will be in, which would in this case be in the positive i direction...

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