1. The problem statement, all variables and given/known data A horizontal rectangular surface has dimensions 3.10cm by 3.05cm and is in a uniform magnetic field that is directed at an angle of 34.5∘ above the horizontal. What must the magnitude of the magnetic field be in order to produce a flux of 4.5E-4 Wb through the surface? 2. Relevant equations Magnetic Flux = BAcos(θ) 3. The attempt at a solution Using the above equation, I solved for B, getting B=Flux/Acos(θ) I then plugged in my numbers: (4.5*10^-4)/((.0305)(.031)cos(34.5)) and got that B should equal 0.5775T. However, it says the answer is wrong, any ideas what I did wrong?
I'd suggest that you make a sketch. You're looking for the flux through a horizontal surface, which means you want the vertical component of the B field... Alternatively, take a vector equation approach and construct vectors for B and the area normal, then expand ##\Phi = \vec{B}\cdot (A\vec{n})##
So how do I go about finding that, though? I understand that I need the vertical component, but I have no idea how to set it up if all I know is the angle?
Make a sketch! Draw a horizontal line to show your area of interest in profile. Draw a vector or two representing the B field. What angle do you need? You can also choose the appropriate trig function and use the angle as given. You want the component of B that's parallel to the surface normal of your area.
Okay, so I would say that B_n (normal component of the B field) = Bsin(34.5), then I can do the flux divided by sin(34.5) times the area, so I have B=4.5*10^-4/((sin34.5)(.031)(.0305)). That way I get B=0.84?