Two very long insulated wires perpendicular to each other in the same plane carry currents as sh

Two very long insulated wires perpendicular to each other in...

Key Concepts

Magnetic Field of a Long Straight Current-Carrying Wire

This concept refers to the magnetic field created by a current flowing through a long, straight conductor. The magnitude of this field at a given distance from the wire is determined by Ampere’s law and is inversely proportional to the distance from the wire. The formula, B = (??I)/(2?r), where ?? is the magnetic constant, I is the current, and r is the distance from the wire, is fundamental in electromagnetism.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the magnetic field created by a current. By pointing the thumb of the right hand in the direction of the conventional current, the curl of the fingers shows the direction of the magnetic field lines encircling the wire. This rule is essential for predicting the orientation of the magnetic fields around current-carrying conductors.

Superposition Principle

The superposition principle states that the net magnetic field produced by multiple sources is equal to the vector sum of the individual fields created by each source. In the context of multiple current-carrying wires, this principle allows us to calculate the total magnetic field at a point by adding the contributions from each wire, taking into account both magnitude and direction.

Vector Addition

Vector addition is the process by which individual magnetic field vectors, which have both magnitude and direction, are combined to obtain a total field. This mathematical technique is crucial when dealing with multiple sources of magnetic fields, as it allows one to compute the resultant magnetic field accurately by considering the components of each individual field.

Transcript

00:01 Hi, in the given problem there are two straight current carrying conductors which are oriented perpendicular to each other.

00:13 This is the first conductor.

00:17 In first case, this first conductor is carrying an electric current of 10 ampere i1 is equal to 10 ampere towards right.

00:32 And the second conductor is carrying a current i2 is equal to 12 ampere in upward direction.

00:43 Now there are two points at which we have to find the net magnetic field along with the direction due to these two current carrying conductors.

00:54 First of all, here at this point p having a distance of 8 cm from the 1st conductor and 15 cm from the 2nd conductor.

01:08 And similarly, another point q here, which is having a distance of 8 cm from the 1st conductor and a distance of 15 cm again from the second conductor.

01:23 So, first of all, we will find magnetic field, net magnetic field at point b at point p and this magnetic field at p will be equal to two magnetic fields at point p.

01:38 One because of the first conductor at p and another because of the second conductor at the same point p.

01:49 Now using bitt and severed law, the expression for magnetic field at a point due to a straight current carrying conductor of infinite length is mu not by 4 pi into 2 i 1 for this first conductor divided by r this distance r1 and for the other one this is mu not by 4 pi into 2 i 2 by r2 we are adding these two magnetic fields here because using right hand thumb rule which says the directions of both b due to 1 at point p and b due to 2 wire 2 at the same point b are into the plane of paper inward into the plane of paper.

03:18 That's why we are adding these two magnetic fields to get the net magnetic field.

03:24 Now plugging in all known values, first of all, this mu not by 4 pi can be taken as a common out along with this two.

03:34 Now for i1, this is 10 ampere and distance r1 that is 8 centimeter, or we can say 8 into 10 is per minus 2 meter plus 15 for r2 and having, sorry, the current is 12 for i2.

03:55 And distance is 15 for our 15 centimeter or 15 into 10 x4 minus 2 meter.

04:01 Now for mu not upon 4 pi this is 10 dash to par minus 7 into 2 and divided by taking this 10 dash per minus 2 also as a common out leaving inside it will be 10 by 8 plus 12 by 15 and solving all these.

04:23 Finally, we get this magnetic field at point p to be equal to 4 .1 into 10 dashpar minus 5 tesla or we can say this is 41 .0 into 10 dashper minus 6 tesla or finally this magnetic field at point p is bp is equal to 41 micro tesla and into the plane of paper.

04:55 And this is the answer for the first part of the problem.

04:58 Then the direction of current in the first conductor is towards rightward.

05:04 Now we have to find using the same method, the magnetic field at point q...

Please give Ace some feedback