Consider thearrangement shown in which a bar can slidewithout friction verticall
ID: 2060867 • Letter: C
Question
Consider thearrangement shown in which a bar can slidewithout friction vertically on the rails. Thecontact of the bar with the rails makeselectrical contact so that current can movethrough the rectangular loop. The resistanceof the rails is zero. The resistance of the baris R and it has a mass m . There is a constantmagnetic field B everywhere into the page asshown. The acceleration of gravity is gdownward. The bar is dropped from restsuch that its initial speed is zero. The verticalrails extend downward forever. For thepurpose of the problem let y = 0 be theposition of the horizontal section of the toprail. Further let the downward direction bethe positive y-direction. Under thesedefinitions the vertical rails extenddownward to plus infinity. Also the bar isdropped fron rest at t = 0.
Explanation / Answer
a) Increases [Area Increases]
b) Anti-Clockwise [Use Lenz' Law]
c) height = gt2/2 , So Area = l*gt2/2
= BA = Bl* gt2/2
= d/dt = Blgt
d) I = /R = Blgt/R
e) FBD, Two forces acting, Mg downward and FB upward due to field.
f) Mg - BIl = Ma,
For terminal velo, a = 0.
Solving, t = MR/ B2l2 ; VT = MgR/2B2l2
g) Integrate f to get differential form
h) Same as f
i) Power (gravity) = Mg * V = M2g2R/2B2l2
Similarly, Power due to resistor can be calculated as I*I*R and value can be compared.