The figure below shows two parallel conducting rails, oriented vertically, conne
ID: 1436486 • Letter: T
Question
The figure below shows two parallel conducting rails, oriented vertically, connected to each other at the top by a wire with a resistance R. A conducting metal rod is oriented horizontally and is in contact with the two vertical rails. The horizontal rod has a length L = 52.7 cm and mass 29.3 g. The rod is released from rest at location A and begins to fall through a region of uniform magnetic field indicated by the shaded area in the figure. When the rod reaches point B, there is an induced current of 2.55 A flowing to the left in the rod, and the rod is moving downward with an acceleration of magnitude 7.85 m/s2. What are the direction and magnitude of the magnetic field in the shaded region?
Please explain, thanks!
Explanation / Answer
i = induced current = 2.55 A
B = magnetic field
L = length
Fb = magnetic force acting upward = i BL
mg = weight of the rod acting downward
force equation for the motion of rod is given as
mg - Fb = ma
mg - i BL = ma
(0.0293) (9.8) - 2.55 B (0.527) = (0.0293) (7.85)
B = 0.043 T
outward to the screen