A conductor carrying a current I=15.0 A is directed along the positive x axis and perpendicular

A conductor carrying a current I=15.0 A is directed along...

Key Concepts

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the resulting vector in a cross product operation, such as when calculating the direction of the force on a current-carrying conductor in a magnetic field. By pointing the fingers of the right hand in the direction of the current and curling them toward the magnetic field, the thumb points in the direction of the magnetic force. This rule is essential for correctly predicting the orientation of forces in electromagnetic systems.

Lorentz Force

The Lorentz force is the force exerted on a charged particle or a current-carrying conductor when it is placed in a magnetic field. For a current-carrying conductor, this force is given by the vector equation F = I (L × B), where I is the current, L is the length vector of the conductor, and B is the magnetic field. This principle is fundamental in electromagnetic applications and helps explain how magnetic fields influence moving charges or currents.

Magnetic Force per Unit Length

Magnetic force per unit length is derived from the total force experienced by a current-carrying conductor when subjected to a magnetic field. It is expressed as F/L = I B sin(?), where ? is the angle between the direction of the current and the magnetic field. This concept simplifies the calculation by normalizing the force over the length of the conductor, and it is particularly useful when dealing with uniform fields and straight conductors.

Vector Cross Product

The vector cross product is an operation on two vectors in three-dimensional space that results in another vector which is perpendicular to the plane containing the original vectors. In the context of electromagnetic forces, the cross product determines both the magnitude and the direction of the force experienced by a current-carrying conductor in a magnetic field. The sine of the angle between the vectors scales the magnitude, ensuring that the force is maximized when the vectors are perpendicular.

Transcript

00:01 All righty, so we've got a problem here where we have a conductor that's carrying a current.

00:05 And i'm just going to very briefly describe that there.

00:07 It's your conductor and it's carrying some sort of current i.

00:11 And it's equal to 15 .0 amps.

00:18 All right.

00:19 And then it's directed along the positive x axis.

00:22 And it's also perpendicular to a uniform b field or magnetic field.

00:27 And we know that the magnetic force per unit length.

00:30 So i can say f sub b per l, right? force per unit length.

00:38 This is equal to 0 .120 newtons per meter.

00:45 And it acts on the conductor in the negative y direction.

00:50 All right, well, number technically this is a vector.

00:52 So we can put some sort of unit here if you want to with a unit vector.

00:55 Question says negative y direction.

00:57 So let's go ahead and we can say you can do like negative j hat.

01:01 If you wanted to all right 1 -20 you can do a negative negative j hat if you technically wanted to but i'm not going to bother writing that i'm going to just keep keep it as it is i just want to have that negative j hat to the right in parentheses just so we know the direction um you know if we want to scroll back up and look at some of the given information so we want to figure out the magnitude and we also want to figure out the direction to the magnetic field um and we want to figure that out in the region through which the current passes.

01:35 So let's dive into this.

01:37 This problem's not too difficult, and it's just our getting into the very basics here of inductors.

01:44 So let's go ahead and start this here.

01:48 I know that my magnetic force, the magnitude of it, i know that's equal to my current multiplied by l here.

02:00 Now what is l? let me finish up with my full expression here real quick, b, sine, theta.

02:06 Okay.

02:07 So what is l? what's that supposed? question what's what is everything here just so we can clear all this up so you have your current i which we have 15 amps the l though i don't don't stress too hard about that right now what you guys want to figure out what we want to focus on here is the fact that we have a force per unit length we already have a sort of ratio as you guys can see if i point here we already have this very fancy ratio right here above us so let's go ahead and try to make use of that...

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