Two long straight wires carry the same amount of current in the directions indicated. The wires

Two long straight wires carry the same amount of current in...

Key Concepts

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the magnetic field produced by a current. By pointing the thumb of the right hand in the direction of the conventional current and curling the fingers, the direction in which the magnetic field circles around the wire is indicated.

Superposition Principle

In a system with multiple current-carrying wires, the net magnetic field at any point is the vector sum of the individual magnetic fields generated by each wire. This principle allows one to calculate the overall magnetic field by independently determining the contribution from each source and then combining them accordingly.

Magnetic Field of a Current-Carrying Wire

A long straight wire carrying a current generates a magnetic field that circulates around it. The magnitude of this magnetic field decreases with distance from the wire and is given by the formula B = (??I) / (2?r), which encapsulates the inverse relationship between the field strength and the radial distance from the wire.

Distance Dependence

The magnitude of the magnetic field from a current-carrying wire diminishes with increasing distance from the wire, following an inverse relationship (1/r). This means that points closer to the wire experience a stronger magnetic influence than those farther away, which is critical when comparing magnetic field strengths at different positions in a multi-wire configuration.

Transcript

00:02 High, in this given problem there are two straight conductors, the long conductors.

00:10 We may assume them to be infinite in length and these two are crossing each other at 90 degree like this.

00:21 The same current is passing through them.

00:24 In the horizontal conductor it is towards left and in the vertical conductor it is towards down and we assume these two conductors to be one and two.

00:46 This is the current in both of them.

00:49 I and here this is first and here this is second.

00:55 Now the observation points, first of all, this is one of the observation point which is at a distance of d from both the conductors.

01:11 Then another observation point b, it is in the opposite side, means below the second conductor, but having the same distances from both the conductors means d, h, and this is b in itself.

01:28 Third observation point is this.

01:31 C, it is having a distance of d from a, means its distance from the conductor will become twice of d.

01:39 And it is having same distance from the conductor from the second conductor and the last observation point d this is also having the distance d from b but it will become twice of d from the first conductor and its distance from the horizontal conductor that is still having the same magnitude same value of d now we will use right hand thumb rule to find the directions of all the magnetic fields at points a, b, c and d due to these two current carrying conductors.

02:58 And applying this rule, first of all, we mention the directions only, the directions of these magnetic fields.

03:06 So, magnetic field at a, point a, due to the wire 1 conductor 1 that will be out of the plane of paper and magnetic field at the same point a due to the second conductor that will be into the plane of paper the two magnetic fields at point a then at point b first magnetic field due to the first conductor that will be out of the plane of paper and at the same point b, the magnetic field due to the second conductor, this will be, this will also be out of the plane of paper.

03:53 Then at the third point c, magnetic field at point c due to the first conductor, that will be out of the plane of paper.

04:18 And at the same point c, magnetic field due to the second wire, that will be into the plane of paper.

04:29 At last magnetic field at d due to the first wire that will be out of the plane of paper and at the same point d magnetic field due to the second wire that will be again this will also be out of the plane of paper and then we use bayard and severed slot to find the magnetic field at any point around a straight current carrying conductor which is given by mu not upon 4 pi into 2 i by r the distance of the observation point so using that b at a due to 1 comes out to be mu not upon 4 pi into 2 i by d and similarly b at a due to the second wire that will also be having the same magnitude and the directions are opposite as we have seen here the two magnetic fields at point a are opposite in direction...

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