textbook eqn derivation - mistake? (1 Viewer)

[anonymoushehe]

the textbook said the perpendicular component of F is given by Fsintheta but am i tripping, the geometry doesnt make sense if theta is defined as the angle between the area vector and the magnetic field lines? this is for the eqn t = nBIAsintheta

 

[Tony Stark]

Very strange, also a confusing depiction of the right-hand rule. I think logically; the force is at a maximum when the coil is perpendicular to the field. So, by trial and error in my calculator, sin(90*)=1 and cos(90*)=0. Thus for the formula to be accurate to real life force must increase with theta, a maximum at 90* (perpendicular) and minimum at 0* (or parallel) to the field.

 

[C2H6O]

the textbook said the perpendicular component of F is given by Fsintheta but am i tripping, the geometry doesnt make sense if theta is defined as the angle between the area vector and the magnetic field lines? this is for the eqn t = nBIAsintheta

View attachment 46842

I hope this is what you were asking but to find F perpendicular look at the diagram. Define the angle alpha, so that theta + alpha =90. That means we can define alpha as the angle on the right side if you extend the coil and the field lines. F is perpendicular to the field lines, so that means that angle labelled purple is theta bc theta and alpha are complementary angles. F perpendicular is in green, and if you look that's a right triangle so using trig F perp is just F sin theta. Hope that makes sense

 

[coolcat6778]

pearson physics 12 is sometimes wrong lol

 

[anonymoushehe]

View attachment 46847
I hope this is what you were asking but to find F perpendicular look at the diagram. Define the angle alpha, so that theta + alpha =90. That means we can define alpha as the angle on the right side if you extend the coil and the field lines. F is perpendicular to the field lines, so that means that angle labelled purple is theta bc theta and alpha are complementary angles. F perpendicular is in green, and if you look that's a right triangle so using trig F perp is just F sin theta. Hope that makes sense

omg you genius