Two parallel wires are 5.00 cm apart and carry currents in opposite directions, as shown in Fig

step 1 Okay, so we're looking at question twenty eight point twelve. We have to parallel wires that are

Two parallel wires are 5.00 cm apart and carry currents in...

Key Concepts

Superposition Principle

The superposition principle states that the net magnetic field at any point due to several sources is the vector sum of the individual magnetic fields produced by each source. This principle is key to solving problems with multiple current-carrying wires or segments, as it allows the combination of fields from parts of the device, taking their magnitudes and directions into account.

Magnetic Field due to a Current-Carrying Conductor

This concept explains that any electric current produces a magnetic field that circulates around the conductor. The magnitude and direction of this field depend on the size of the current and the distance from the wire. The Biot–Savart Law is typically used to calculate the field produced by an individual segment of current, and Ampère’s law is applied to symmetric configurations.

Magnetic Field due to a Finite Current Segment

Unlike an infinitely long current-carrying wire, the magnetic field produced by a finite segment is calculated using a modified form of the Biot–Savart Law. In such cases, the field depends on the angles subtended by the ends of the segment at the observation point. This is important when dealing with finite segments placed at specific distances from the point of interest.

Right-Hand Rule

The right-hand rule is a method used to determine the direction of the magnetic field produced by a current. When you point your thumb in the direction of the current, your curled fingers show the direction of the magnetic field around the wire. This rule is essential for understanding how the magnetic fields from different segments interact when currents are in various directions.

Transcript

00:01 Okay, so we're looking at question twenty eight point twelve.

00:04 We have to parallel wires that are five centimetres apart, so each one is going to be two and a half centimeters from this point.

00:14 Pain, um, and we have currents in each of these wires.

00:21 The first current is going is twelve amps going to the right and then the bottom wire is twenty four amps moving to the left and were asked to find the magnitude and direction of the magnetic field at point peak.

00:37 So let's first start thinking about the direction of the magnetic field.

00:41 So, looking at the top wire here, we see that the field is pointing to the left to the right.

00:49 And so, using the right hand rule, if we point our thumb in the direction of the current than our figures are going to curl into the page at point p.

00:59 So the magnetic field is pulling into the page from this top current from the bottom current that's moving to the left again.

01:08 If you use the right hand rule, we point our thumb in the direction to the left and then our finger they're going to curl into the board so again at point p, that's causing a current directly straight into the page.

01:23 So that's the direction.

01:24 And that's convenient because it means we're going to be able to simply add the magnitude of the current from of the magnetic field from each of these two wipers.

01:34 So to find the magnetic field from a segment of current, we need to use the beyonce of our law, which is i've been right up over here.

01:45 So the magnetic field is going to be you, not over for pie when our constant you not, and then the current thief segment of length of the wire and then sine of the angle here, this angle file, this is the angle that we're gonna want.

02:03 We want the angle between the current and the direction, uh, pointing to the point that we want ah, and then our is going to be the actual distance.

02:14 So that's going to be our eight centimeters here.

02:17 So going through implying this and let's just do this for wire one.

02:23 So that's hop current appear of twelve hams, so copying our equation over here we have the current, uh, in this case is going to be twelve ants b d l that we want to use...

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