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

 

[wizzkids]

this is for the eqn t = nBIAsintheta

Watch out for this one! In mathematics we define the vector for a plane as the perpendicular to the plane. In at least one recognised Physics textbook, they take the angle of the coil to be the angle between the sides of the coil and the B-vector. Clearly these are not the same definitions and you need to watch out for this one. In the HSC Physics equation sheet, it says and they are defining as the angle between the normal to the plane of the coil and the B-vector.