A wire 2.80 m in length carries a current of 5.00 A in a...

A wire 2.80 m in length carries a current of 5.00 A in a region where a uniform magnetic field has a magnitude of 0.390 T. Calculate the magnitude of the magnetic force on the wire assuming the angle between the magnetic field and the current is (a) $60.0^{\circ},$ (b) $90.0^{\circ},$ and (c) $120^{\circ}.$

Key Concepts

Magnetic Force on a Current-Carrying Wire

This concept involves the force exerted on a wire carrying an electric current when it is placed in a magnetic field. The force is given by the formula F = I L B sin(?), where I is the current, L is the length of the wire, B is the magnetic field strength, and ? is the angle between the current direction and the magnetic field. Understanding this formula is essential in electromagnetism as it describes how magnetic fields interact with moving charges in conductors.

Angle Dependence via the Sine Function

The sine function in the magnetic force equation indicates that the magnitude of the force depends on the sine of the angle between the direction of the current and the magnetic field. The force reaches its maximum when the sine of the angle is 1 (at 90°), and it decreases as the angle deviates from 90°. This concept is important because it shows how the orientation of the wire relative to the magnetic field affects the resulting force.

Uniform Magnetic Field

A uniform magnetic field is a field in which the magnetic force is constant in magnitude and direction at every point in a given region. This simplifies the calculation of forces on current-carrying wires, as the magnetic field does not vary along the length of the wire, allowing the direct application of the magnetic force formula without additional complexity.

Transcript

00:01 All righty, so in this problem, we got a wire, and we know that the wire has a length of 2 .8 meters.

00:10 L equals 2 .80 meters.

00:15 And we know there's a current of 5 amps, and we know that there's a magnetic field of 0 .390 teslas in that region.

00:22 So we can just very quickly put out of our eye there.

00:25 We also have a magnetic field.

00:28 E, and that equals 0 .390 teslas.

00:32 All right.

00:37 So we're going to calculate the magnetic force on the wire, and we're going to just do that, though, assuming some different case scenarios.

00:43 First case scenario, the angle, i guess, technically speaking with this problem, i have to be very clear about something.

00:49 We don't know this.

00:51 We technically don't know that.

00:53 We just know there's some b -field vector.

00:55 I want to make sure i'm clear about that.

00:57 So, a, theta equals 60 degrees, b, theta equals 90 degrees, and see theta equals 120 degrees.

01:09 Our job is to figure out the magnetic force for each of those situations, and then we'll record them, and then we'll be done.

01:16 So let's jump right in.

01:19 Part a here.

01:20 We know that force of the magnetic field.

01:22 This is the same equation we'll be using for all this stuff here...

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