I’m a senior in high school and I don’t know how to choose sin or cos in physics problem. For the most part I memorised them. For example, why is the flux of a magnetic field = BAcos(angle) and why is the electromagnetic force = ILBsin(angle).
The last two years weren’t normal as we studied online so it’s highly appreciated if someone can eli5 and fill in the gaps for me.
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The magnetic flux is a number (scalar) that tells you how much magnetic field lines are going through a surface.
Say for example that there is a uniform magnetic field present in the z-direction in your room (so the magnetic field is pointing upwards from the ground in standard 3D space). Say you have a sheet of paper that is lying on the ground. You then have a magnetic flux going through the sheet of paper that is equal to the product of B and A, where B is the magnetic field strength and A is the area of the paper. You can imagine this as the amount of magnetic field that your sheet of paper is “catching”.
If you now hold the paper on its side, none of the magnetic field lines can go through the sheet. The sheet cannot “catch” any magnetic field lines since they are moving parallel to the sheet. The flux is thus equal to zero.
Since the direction of both the magnetic field lines and the sheet of paper are important to determine the flux, the orientation of the field lines with respect to the paper needs to be known in order to calculate the flux. Because it is easy to do so, we have decided to give the orientation of an area by its normal vector. The normal vector is simply the vector that is perpendicular to the sheet.
Like I said, the flux gives a number and is the result of two vectors, namely the magnetic field strength B and the area A. The flux is then simply defined to be the inner product of B and A, which becomes:
Psi = B*A*cos(alpha), where Psi is the flux and alpha is the angle between the magnetic field lines and the normal vector.
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