A square loop of wire consisting of a single turn in...

Name: A square loop of wire consisting of a single turn in perpendicular to a uniform magnetic field. The square loop is then re-formed into a circular loop, which also consists of a single turn and is also perpendicular to the same magnetic field. The magnetic flux that passes through the square loop is 8.83 Wb. What is the difference in the flux between the circular and square loop?
Uploaded: 2023-03-22T14:42:19-08:00
Duration: 6 min 2 s
Channel: Madhur L
Description: A square loop of wire consisting of a single turn in perpendicular to a uniform magnetic field. The square loop is then re-formed into a circular loop, which also consists of a single turn and is also perpendicular to the same magnetic field. The magnetic flux that passes through the square loop is 8.83 Wb. What is the difference in the flux between the circular and square loop?

A square loop of wire consisting of a single turn in perpendicular to a uniform magnetic field. The square loop is then re-formed into a circular loop, which also consists of a single turn and is also perpendicular to the same magnetic field. The magnetic flux that passes through the square loop is 8.83 Wb. What is the difference in the flux between the circular and square loop?

Transcript

00:02 Hello, in the question we have given a square loop of wire consisting of a single turn.

00:06 So there is a single turn.

00:08 So this wire, there is a square loop of wire.

00:12 So if it is a square loop, so we can consider that the side is a.

00:17 So it consists of a single turn.

00:19 So n is equal to 1.

00:22 In a perpendicular uniform magnetic field, so this is placed in a perpendicular magnetic field.

00:29 So if this is the coil, so the magnetic field is either coming out or wrong.

00:32 Going in so let's say it is placed in a magnetic field like this i'm not drawing all the fields so just to represent now this square loop is then reformed into a circular loop so now this square loop is then reformed to a circular loop so this circular loop is there so we can consider that this is the radius of the circle now and again the same magnetic field is there so only we have changed the shape of this loop.

01:05 So the magnetic field is still coming out of the page.

01:08 So the magnetic flux that passes through the square loop.

01:12 So the magnetic field flux that is passing through the square loop.

01:17 So 5b .s.

01:20 Let us say 5b .s is the magnetic flux passing through this square loop.

01:24 So that is equal to 8 .83 webbers.

01:30 So this is given.

01:31 Now what they are asking what is the flux difference what is the difference in flux between the circular loop and the square loop so in order to find this let us see what is flux so the magnetic flux is given by close integral b bar dot d s bar so if we integrate this so this be integration of ds it will be now ds depends on the surface which we consider so this is 5 b so now this phi b we will use for the square loop and the circular loop.

02:11 So for square loop, for square loop, if we write this, so 5 b s will be equal to b.

02:22 Now integration of ds.

02:24 So it will be the area of this square.

02:26 So that is a square.

02:28 So this is the magnetic flux for the square loop.

02:32 For for circular loop, for the circular loop, this 5.

02:40 B s, phi b, c we will write for the circular loop.

02:46 So that will be b times area is pi r square.

02:50 Now we don't know what is r.

02:54 Although we don't know what is a, but we know the relation between this phi b and a.

02:58 So let us first find out...