Two insulated wires, each 2.40 m long, are taped together to form a two-wire unit that is 2.40 m

Two insulated wires, each 2.40 m long, are taped together to...

Key Concepts

Lorentz Force on a Current-Carrying Conductor

This concept describes the magnetic force exerted on a wire when it carries an electric current and is placed in a magnetic field. It is governed by the equation F = I L B sin(?), where F is the force, I is the current through the conductor, L is the length of the conductor in the magnetic field, B is the magnetic field strength, and ? is the angle between the direction of the current and the magnetic field. This principle is fundamental in understanding how moving charges interact with magnetic fields.

Angular Dependence of Magnetic Force

The magnitude of the force on a current-carrying wire is not constant but depends on the sine of the angle between the wire and the magnetic field. The term sin(?) in the Lorentz force equation highlights that the force reaches its maximum when the wire is perpendicular (? = 90°) to the magnetic field and drops to zero when it is parallel (? = 0°). This angular relationship is key when analyzing forces in various orientations.

Superposition of Magnetic Forces

When multiple current-carrying wires are present in a magnetic field, each experiences its own magnetic force according to the Lorentz force law, and the net force on the system is determined by the vector sum of these individual forces. In cases where the currents are in opposite directions, the forces may oppose each other, and their magnitudes need to be subtracted to determine the resultant force on the system. This concept is crucial for analyzing systems with multiple interacting conductors.

Transcript

00:01 Alright, for this one let's start by drawing a little diagram of the situation that we have.

00:06 So we're told we have two wires.

00:11 I'm going to number the wires just to keep them separate.

00:14 We have wire 1 and wire 2.

00:19 Now we're told that they both have currents, but they're in opposite directions.

00:26 So now this is arbitrary.

00:27 I'm just going to pick up for 1 and down for 2, just to show that they are in opposite directions.

00:35 Also told that they are in a magnetic field that is 60 degree there are 65 degrees to the wires and this this magnetic field is present everywhere around the wire so if we were to draw a orthogonal line to the wires this angle here would be 65 and this field is everywhere everywhere present along the wires at the same angle.

01:24 Okay, all the things that we are given, we're given the length of both wires.

01:29 They are equal.

01:33 So we don't need to worry about two different lengths.

01:36 We are given the current for the first one, layer one, which i will call i1 for current one.

01:47 Current one.

01:48 We are given the magnetic field, the magnitude of the magnetic field and the direction, which we have is our angle.

01:56 We're given b, and we are given the net force, and we'll get into exactly what that means in a little bit here.

02:08 We're going to call it f subnet.

02:15 Okay, so we have all of these variables here.

02:21 It's very likely that the equation that we're going to use that involves all of these is the equation for the force, which says that the force is equal to the current times the length through which the current is traveling.

02:40 The current i times l times the magnetic field b, sign of the angle between them or sign of theta.

03:02 So this is the equation that we're going to want to use here.

03:07 So now how do we incorporate this net force? so that means that's the force over the entire system.

03:16 That's the force both of these two wires together experience.

03:20 So now we have one wire that goes that has a current flowing up and one wire that has a current flowing down.

03:26 This means that the net force is going to be the sum of these two, but the force is going to be in opposite directions.

03:34 So what that means is our net force in this case is equal to some of these two, but because they're in opposite directions, we're going to have a minus sign.

03:51 So now, because this is physics, we get to decide what directions we want to be positive and what to be negative.

03:58 And it doesn't matter what we choose.

04:01 We just have to keep it consistent.

04:03 We could say up is positive, and down is positive.

04:08 But it's just kind of a general idea to have down as negative.

04:13 That's how a lot of things have it.

04:15 If you want to keep it similar to a lot of things you've seen before, we can have down as negative.

04:19 And what that means is, so f1 is for the first wire, what that would mean to have down negative is that f1 or the f net is equal to f1 minus f2...

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