A long, straight wire carrying a current of 305 A is placed in a uniform magnetic field that has

A long, straight wire carrying a current of 305 A is placed...

A long, straight wire carrying a current of 305 $\mathrm{A}$ is placed in a uniform magnetic field that has a magnitude of $7.00 \times 10^{-3}$ T. The wire is perpendicular to the field. Find a point in space where the net magnetic field is zero. Locate this point by specifying its perpendicular distance from the wire.

Key Concepts

Magnetic Field from a Long Straight Wire

This concept involves the magnetic field produced by a steady current flowing through a long, straight conductor, which is given by the formula B = ?0I/(2?r). It explains how the field's magnitude decreases with distance from the wire, and it provides insight into the field’s circular nature around the current-carrying wire as determined by the right-hand rule.

Uniform Magnetic Field

A uniform magnetic field is one in which the magnitude and direction of the field are constant at all points in space. This concept is essential in understanding how an external magnetic field can interact with other magnetic fields, such as those produced by a current-carrying wire.

Superposition Principle of Magnetic Fields

The principle of superposition states that when multiple magnetic fields are present, the total magnetic field at any point is the vector sum of the individual fields. This principle allows one to analyze scenarios where fields from different sources can cancel each other out, leading to points where the net magnetic field is zero.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the magnetic field around a current-carrying wire. By pointing the thumb of the right hand in the direction of the current, the curl of the fingers indicates the direction of the magnetic field lines. This rule is crucial for understanding field orientation and the conditions required for cancellation.

Transcript

00:01 Okay, so this problem, the setup that we have or the situation that we have is a long straight wire that is placed in an external magnetic field.

00:11 This magnetic field has no relation to the wire, meaning it's not created by the wire.

00:19 It's from something else that we don't know.

00:21 It's just there.

00:22 This wire is in this field.

00:28 And we know from our extensive research on magnetic fields that the wire with a current in it will produce a magnetic field.

00:43 So we have this external magnetic field that is perpendicular to the wire or perpendicular to the current traveling in the wire.

00:54 And we are tasked with finding the net magnetic field where it's equal to zero.

01:02 B net, we want to find where b net is equal to zero.

01:14 So first we need to understand what that means exactly.

01:17 So now the wire here is going to have its own magnetic field that moves around this way.

01:31 So we need to find the points where the magnetic field from the wire cancels with the magnetic field from this external force, or this external, whatever is creating it.

01:43 So if we take a point here, this point is still going to have this, the magnetic field i have in green, pushing it up if it's a charge.

01:58 And it will have the magnetic field from the wire pushing it down.

02:14 So we need to find what this distance is from the wire.

02:20 And we have an equation for what the magnetic fields from a wire looks.

02:25 Like.

02:31 So the magnetic field created by a current carrying wire is equal to mu not, the constant, times the current in the wire, divided by 2 pi times the distance or the radius from the wire, times the radius.

03:06 So that's our equation for the magnetic field from the wire...

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