Hello, students, now let’s study magnetic flux before we move onto electromagnetic induction. Now same as electric flux, magnetic flux is also defined as the surface integral of the normal component of the magnetic field passing through that surface. And here the SI unit of magnetic flux is weber. So the mathematical formula is flux is integral B.ds. Like in electric field we had seen flux was E.ds. Here it is integral B.ds. So if this is a surface, the normal component of B.product takes care of that. So flux the mathematical formula is integral B.ds. Now B is the magnetic field vector and ds is basically the area vector. Now if we have an open surface the area vector can be taken either in the upward direction or in the downward direction, so there are two possibilities. But if we have a closed surface we always take the area vector as the outward normal. So if we have an open surface you have two choices, if we have a closed surface only take the outward normal as the area. Now see, if the magnitude of magnetic field that is B is constant and also the angle between B and area is constant, then we can simplify our equation. See flux is integral, B can be taken out of the integral. So B.integral ds. Now if we integrate ds, ds is the area vector. So if you integrate ds we will get the area vector so flux is B.A. And since the angle is constant we can also write flux is BA cos theta. So this is also the formula for flux but this is valid only when B is constant and the angle between B and area is constant over the entire surface. Then we can use this simple formula otherwise we have to use flux is integral B.ds.

Now let’s calculate magnetic flux in some simple situations. So in this figure you see there is an area and magnetic field lines are passing through that area. What we can do is first of all draw the area vector so area vector we had drawn perpendicular to the surface. We can also take the area vector towards the left, it is upto you. Now sometimes the diagram can be drawn like this, this is the side view. If you see this diagram from the front we can draw like this. If you see the same diagram from the left hand side or basically call it the front view, then see the magnetic field lines are crossing the area perpendicularly. So this is also a way of drawing. Now flux has two formulas, integral B.ds or BA cos theta. Now how do we decide what formula to use and how to calculate flux? So basically follow three simple steps. First check the magnetic field is constant over the entire surface. So in this question, see B is constant over the entire surface, okay, fine. Now let’s move on to checking the angle between B and area vector. So if you see the angle between B vector and area vector is 0 degree. So angle is 0 which is also constant, then find the flux. So flux is BA cos 0 that means flux is equal to B into A.

Let’s take another situation, here the area is tilted a bit, B is horizontal and which is constant. So again if you draw the area vector we can draw perpendicular to the surface. The other possibility is also outward but any one you can choose. Now if we mark the angle suppose the angle of the area vector was theta from the vertical. So just calculate the angle between area vector and B vector. So we can see the angle between area and B is again theta. So B is constant over the entire surface, first step is valid. Angle between B and A is also constant theta. So we can write flux is equal to BA cos theta.

So basically this thing we have studied in electrostatics, so in magnetism also or EMI also we need the concept of flux. We can also see, if we divide the area or basically take the component one will be A cos theta and other will be A sin theta. So the component of area along the field will not contribute in flux, because the normal will be perpendicular to B. Only the component of area which is perpendicular to B contributes in the flux, so we can also write flux is equal to B into A perpendicular. In this case A perpendicular is A cos theta. So flux will be BA cos theta.

Now let’s take another situation, let’s take it one by one. See this is an area vector and D is as shown in the figure. Now directly you can see, D is constant over the surface, now angle between D and A, see the area vector is inside the plane or outside the plane. So you can take any of the two options, let’s take the area vector out of the plane. So angle between B and A is 90 degrees, you can see in the diagram the angle between B and A is 90 degrees. So we can write flux is BA cos theta that means BA cos 90 which is equal to 0.

Let’s take this situation, now see the magnetic field lines are inside the plane. Area vector can be taken outside or inside. See B is constant over the entire surface, the angle between B and area vector is either 180 or 0 degree depends on how you take the area vector. So we have taken the area vector like this, the angle is 180 degrees, so flux is BA cos 180 that means minus BA.

Let’s take this situation, see this is a tricky situation, this 30 degrees is useless because if you see angle between B and area vector is basically 90 degree. B is constant over the entire surface that is very obvious. Now angle between B and A is again 90 degrees because if you draw any line the plane is perpendicular, the area vector and B vector plane is perpendicular. So if you draw any line at 30 degrees, 0 degrees, 90 degrees, it will all be perpendicular to the area vector. So again flux is equal to BA cos 90 that means zero.

Thank you.

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