in this problem we have a circular coil with a radius of 25 centimeters and we have a magnetic field that is perpendicular to the face of the coil and we need to calculate the magnetic flux in this coil the magnetic flux is represented by this symbol it's b times a and this is the component of the magnetic field that is perpendicular to the plane of the coil and so for this problem the magnetic flux is going to be b times the area of the circle which is pi r squared so the magnetic field is 20 tesla and the radius is 25 centimeters which is 0.25 meters squared so the magnetic flux is 3.93 tesla times square meters which you could simply represent that as a weber so one weber is one tesla times one square meter so this is the standard unit for the magnetic flux so that's the answer or you can leave it like that if you want number two a magnetic field of 30 tesla is directed parallel to the face of a square coil calculate the magnetic flux so let's say this is the square coil and this time the magnetic field is not in perpendicular to the face of the coil rather it's parallel to the face of the coil so it's going in that direction what's the magnetic flux because it's not going through the surface of the square coil rather it's just like passing by it the flux is going to be zero the flux is equal to the component that's perpendicular to the coil times the area and there is no perpendicular component so therefore that part is zero so the flux is zero in this case or zero webbers the perpendicular component it turns out is b cosine theta so you can represent the flux equation like this the magnetic flux is b times a times cosine of theta and so what's theta theta is the angle between the normal line which is perpendicular to the surface and the angle i mean nb so this angle here between the magnetic field vector and the normal line that's theta so in this example theta is 90. so we have 30 tesla that's the magnetic field times an area of 0.10 meters squared that's left times width times cosine of 90 degrees since they're perpendicular to each other now cosine of 90 is zero and so that's why the whole thing is zero so the flux is zero and the last problem the magnetic field was parallel to the normal line and so the angle between them is 0 degrees and cosine of zero degrees is one and so that's why the magnetic flux in the last problem was simply b times a because this was completely like perpendicular to the face of the coil now let's move on to number three so our goal in this problem is to calculate the magnetic flux through each square so you need to know which angle to use when dealing with these types of problems so the magnetic flux is going to equal the magnetic field times the area of the coil times cosine of theta now keep in mind theta is between the normal line and the magnetic field so in the first problem on the left theta is 40 degrees now what about on the right what's theta so here's the normal line and here is the magnetic field so theta is complementary to that angle it's 90 minus 30 which is 60 degrees so make sure you choose the right angle otherwise you can get the wrong answer so for the first one it's going to be the magnetic field which is 10 tesla multiplied by the area since we're dealing with a square the area is just going to be length times width so 50 centimeters is 0.5 meters so 0.5 times 0.5 and then multiplied by cosine of 40 degrees so you should get 0.766 webers for the magnetic flux of the first example now go ahead and try the next example let's use the exact same formula so b is still going to be 10 the area is still going to be 0.5 times 0.5 which is 0.25 square meters but this time we're going to use cosine of 60 as opposed to cosine 30. and cosine 60 is a half a half times 0.25 is 0.125 and then times 10 will give us a magnetic flux of 1.25 webbers or tesla times square meters so now you know how to calculate the magnetic flux through a surface it's simply the magnetic field times the area times cosine theta where the angles between the magnetic field and the normal lines so just don't forget that so thanks for watching you