(II) A long pair of insulated wires serves to conduct 28.0 A of dc current to and from an instru

step 1 We want to find the magnetic field that's made by two wires. And so we know that the current in

(II) A long pair of insulated wires serves to conduct 28.0 A...

(II) A long pair of insulated wires serves to conduct 28.0 $\mathrm{A}$ of $\mathrm{dc}$ current to and from an instrument. If the wires are of negligible diameter but are 2.8 $\mathrm{mm}$ apart, what isthe magnetic field 10.0 $\mathrm{cm}$ from their midpoint, in their plane (Fig. 36$) ?$ Compare to the magnetic field of the Earth.

(II) A long pair of insulated wires serves to conduct 28.0 $\mathrm{A}$ of
$\mathrm{dc}$ current to and from an instrument. If the wires are
of negligible diameter but are 2.8 $\mathrm{mm}$ apart, what isthe magnetic field
10.0 $\mathrm{cm}$ from their midpoint, in their plane (Fig. 36$) ?$
Compare to the magnetic field of the Earth.

Key Concepts

Magnetic Field from a Long Straight Conductor

This concept involves calculating the magnetic field produced by a straight, current-carrying wire using the formula B = ??I/(2?r). It stems from the Biot–Savart law and Ampere's law, highlighting how the field strength decreases inversely with distance from the wire.

Superposition Principle in Magnetism

Magnetic fields are vector quantities, which means that when multiple sources of magnetic fields are present, the net field at any point is the vector sum of the individual fields. This principle is essential for analyzing the resultant magnetic field when more than one current-carrying conductor influences the region.

Right-Hand Rule

The right-hand rule is a convention used to determine the direction of the magnetic field around a current-carrying conductor. By aligning the thumb with the direction of current flow, the curled fingers indicate the direction in which the magnetic field circulates.

Transcript

00:01 We want to find the magnetic field that's made by two wires.

00:05 And so we know that the current in these wires must be going in opposite directions, since we're told that this is wires that are carrying current to an appliance and then back away from the appliance.

00:16 So the net change in charge has to be zero.

00:19 So one's taking a two, one's going the away.

00:21 So they both then are going to have the same value of i, which we're told as two amps.

00:27 And then we're told the wires are separated by a distance 2 .8 millimeters.

00:30 I've called that d.

00:32 And then it's a distance r from the center of the two wires, which is 10 centimeters.

00:37 And that's where we want to find what the magnetic field is.

00:40 So we can just say then our magnetic field is going to be the sum of the magnetic field made by each of these two wires.

00:49 And i don't think we're actually told that this distance is off to the right.

00:53 It could be to the left.

00:54 So really, we're just going to find the magnitude of the magnetic field and not worry about the sign.

00:59 So we're going to have, from what, wire 1, mu not i 1 over 2 pi r1.

01:08 And then regardless of whether this point is on the right or the left, these two wires will have magnetic fields of opposite signs.

01:16 So that's really all that matters here for the magnitude.

01:19 And so that will then be mu not i2 over 2 pi r2.

01:25 So that's just sort of the most general form, but we can simplify that a lot in this situation...

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