In the figure, four long straight wires are perpendicular to...

Name: In the figure, four long straight wires are perpendicular to the page, and their cross sections form a square of edge length a = 21 cm. The currents are out of the page in wires 1 and 4 and into the page in wires 2 and 3, and each wire carries 28 A. What is the magnitude of the net magnetic field at the square's center?
Uploaded: 2022-04-28T07:14:37-08:00
Duration: 6 min 26 s
Channel: Madhur L
Description: In the figure, four long straight wires are perpendicular to the page, and their cross sections form a square of edge length a = 21 cm. The currents are out of the page in wires 1 and 4 and into the page in wires 2 and 3, and each wire carries 28 A. What is the magnitude of the net magnetic field at the square's center?

In the figure, four long straight wires are perpendicular to the page, and their cross sections form a square of edge length a = 21 cm. The currents are out of the page in wires 1 and 4 and into the page in wires 2 and 3, and each wire carries 28 A. What is the magnitude of the net magnetic field at the square's center?

Transcript

00:01 Hello students.

00:01 In this question the current in each wire is given by i is equal to 28 ampia and it is a square and the length of the square is given as 21 centimeter which is equal to 0 .21 meter.

00:22 In order to find the direction of the magnetic field we will use the thumb rule right -hand thumb rule we have to find what is the net force at all using the right hand thumb rule we can find what is the force due to each of these charges it is given that charges two and three the magnetic field is into the page and for one and four the magnetic field is perpendicularly out of the page hence the magnetic field in this case using the right hand thumb rule will be in this direction.

01:12 Point your thumb in the outside the plane of the paper perpendicularly up so you will get b is equal to this.

01:26 Now similarly for this point is also the magnetic field is in this direction now for this point, the magnetic field for the charge for the point three, the magnetic field is going to be in this direction and the magnetic field here is going to be in this direction.

01:46 Let us name them as a, b, b, b and d.

01:55 So the magnetic field b, a is going to be equal to b b is going to be equal to b.

02:06 Is going to be equal to bd which we say is equal to b the magnitude of the magnetic field at each of these points is going to be the same because the current is same in all the four wires so the magnetic field that oh let me represent it out here is going to be these are the two diagonals is going to be bc is going to act in this direction and b, a is also going to act in this direction using this right -hand thumb rule.

02:53 Similarly, b -d and b -b will act along this.

03:01 So this is where the magnetic field at zero acts.

03:06 And we have to find what is this resultant of all these.

03:15 Forces at o this is point o and this angle is going to be 45 degree because this entire angle is 90 degree.

03:32 Now the magnetic field b we know is given by mu not i by twice by r where r is the distance d -o or d -o which we know is equal to mu not twice pi is 4 pi into 10 to the power minus 7 i is 28 ampia divided by twice pi and r is 0 .21 root 2 divided by 2 .2 .2 is 0 .21 root 2 is the length of the diagonal which you can find using the pythagoras theorem, which is equal to 3 .77 into 10 to the power minus 5 tesla.

04:54 Now we have already explained how the field works at o...

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