phy em calculating problem

1) 參見下圖:

圖片參考：http://i1191.photobucket.com/albums/z467/robert1973/Apr11/CrazyEM1.jpg

You should consider, by Flemming's left hand rule, the magnetic force on the wire is horizontal but NOT vertical.

So in order to maintain the wire in equilibrium:

R cos 20 = mg = 5N

R = 5.32 N

Also since the forces are in equil. and W and FM are perp., we have:

W2 + FM2 = R2

FM = 1.82 N

Hence 0.2 x 5 x B = 1.82, giving B = 1.82 T

2) Magnetic flux density inside the solenoid B = 4π x 10-7 x 2000 x 3 = 2.4π x 10-3 T

Hence force on wire BC = 2.4π x 10-3 x 0.03 = 3 = 2.16 π x 10-4 N

giving a moment of 2.16 π x 10-4 x 0.1 = 2.16 π x 10-5 Nm

So the position of the rider is at (2.16 π x 10-5)/(0.0005 x 10) = 0.136 m

2011-04-29 09:08:56 補充：
4) 個 free body diagarm 有 mg, magnetic force by the B-field (always pointing away from the centre of the track) and normal reaction from the track.

d) When the sphere reaches M, the velocity is:

v = √(2gh) = √20

So the centripetal force required is mv^2/r = 0.004 N

2011-04-29 09:10:52 補充：
4d) (cont'd)

The magnetic force is Bqv = 2 x 100 x 10^-6 x √20 = 8.94 x 10^-4 N

Thus the normal reaction on it is:

0.004 + 8.94 x 10^-4 = 4.89 x 10^-3 N