How to prove the radius of curvature at any point on a line?

AI Thread Summary
To prove the radius of curvature at any point on a line in a magnetic field, one must evaluate the derivative dB/ds, where s is the distance along the field line. The formula for the radius of curvature is given by p = B^3 / [B x (B * del) B]. The discussion emphasizes the importance of understanding the relationship between magnetic induction B and its curvature properties. Participants are encouraged to focus on the mathematical derivation without creating multiple threads for the same question, adhering to forum policies. This approach will help clarify the concept of curvature in magnetic fields.
catheee
Messages
4
Reaction score
0
How to prove the radius of curvature at any point on a line?

In a magnetic field, field lines are curves to which the magnetic induction B is everywhere tangetial. By evaluating dB/ds where s is the distance measured along a field line, prove that the radius of curvature at any point on a line is given by

p= B^3 / [ B x( B * del) B]

where do i start with this?? I have no idea what to do
 
Physics news on Phys.org
Please do not create multiple threads for the same question. It is against forum policy.
 
I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
Thread 'A cylinder connected to a hanging mass'
Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
Back
Top