A 15-g 10 -cm-long wire is suspended horizontally between the poles of a horseshoe magnet. When

A 15-g 10 -cm-long wire is suspended horizontally between...

Key Concepts

Magnetic Force on a Current?Carrying Conductor

This concept describes the force experienced by a wire carrying an electric current when placed in a magnetic field. According to the Lorentz force law, the magnitude of the force is given by F = I L B sin?, where I is the current, L is the length of the conductor, B is the magnetic flux density, and ? is the angle between the current direction and the magnetic field. This principle is central in understanding how the interaction between electricity and magnetism can exert mechanical forces.

Force Equilibrium and Balance

In this context, the concept involves balancing the upward magnetic force against the downward gravitational force acting on the wire. The weight of the wire (mg) must be overcome by the magnetic force for the wire to 'jump up'. By equating these forces, one can obtain quantitative insight into the strength of the magnetic field, making this a practical application of balancing forces in physics.

Magnetic Flux Density Estimation

This concept involves determining the strength of a magnetic field, typically measured in teslas (T), by using the measured forces and known parameters of the system. By rearranging the force equation F = I L B sin? and equating the magnetic force to the gravitational force on the wire, one can solve for B. This illustrates how experimental observations, such as the motion of the wire, can be used to indirectly measure fundamental properties of a magnetic field.

Transcript

00:01 In this problem, a horseshoe magnet, and suspended between this horseshoe magnet will be a wire that's carrying some current, or at least is conductive, and we'll be able to apply current to it.

00:18 So let's say this is the north, south ends of our magnets, so this is magnetic field in this region here, pointing from the north to south end of the magnet.

00:30 And then we have some wire suspended horizontally between the north -south pole of the magnets.

00:41 We're told that when a current is passed through this wire, so some current i passed through this wire, it jumps straight up and out of the magnet.

00:54 So that's telling us that there's some force, fb, magnetic force, that acts on that wire, when a current runs through it and forces it out of the magnet.

01:08 Well, we can find out what the strength of the magnet of the magnet itself needs to be in order to have a force powerful enough to shoot the wire up into the air.

01:19 We know that right now the only other forces acting on this wire would be gravity, fg, and the force of gravity on the wire is equal to its mass times acceleration due to gravity.

01:35 So we'll use 15 times 10 to the minus 3 kilograms.

01:45 I want to use our si units here, kilograms, and then multiplied by force of gravity, 9 .8 newtons per kilogram.

01:59 You might also see that as meters per second squared.

02:01 It works out to be the same thing.

02:04 And then we just plug that into our calculator and get that the force, of gravity acting on 0 .147 newtons.

02:19 So that's gravity pulling down on the wire.

02:23 Fb then needs to be greater than that force in order to overcome gravity.

02:33 We know that fb is given by this equation be equals il b sine theta.

02:44 The theta is this angle between the magnetic field and the direction of the current...