1) Using the diagram, a metal rod is pushed by force F at constant speed v = 28.

Question

1) Using the diagram, a metal rod is pushed by force F at constant speed v = 28.2 m/s along frictionless rails distance 2.32 cm apart. The rod passes through magnetic field 5.56 T pointing downward, and the resistance of the circuit (with the light bulb) is 91.3 . Find F, the magnitude of the force, in N, needed to push the bar at constant speed.

[If I could also please have help on this one too]

2) A "long" solenoid of length 3.16 m has radius 48.5 cm, 3,625 turns and carries current 11.3 A. A wire carrying current 48.9 A runs across the diameter at the center of the solenoid. Find the magnitude of the force on this wire, in N, due to the currents.

Explanation / Answer

Given,

v = 28.2 m/s ; L = 2.32 m ; B = 5.56 T ; R = 91.3 Ohm

We need to find the force F.

becaues of the motion of the rod an emf will be induced. The magnitude of the emf will be:

e = B L v

from Ohm's law,

e = IR => I = e/R = B L v/R

magnetic force on the rod is given by:

F = B I L

F = B (B L v)/R L = B^2 L^2 v/R

F = 5.56^2 x 0.0232^2 x 28.2/91.3 = 0.00514 N

Hence, F = 0.00514 N = 5.14 x 10^-3 N = 5.14 mN

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