Question

A rod of length L and electrical resistance R moves through a constant uniform magnetic field B, perpendicular to the rod. The force that must be applied by a person to keep the rod moving with constant velocity v is:

a) 0
b) BLv
c) BLv/R
d) B²∙L²∙v/R
e) B²∙L²∙v²/R

Answer 1

The force to be applied to keep the rod moving with constant velocity through a magnetic field is given by the expression d)B2L2v/R.

Step-by-step explanation:

The student has asked about the force that must be applied by a person to keep a rod moving with constant velocity v through a constant uniform magnetic field B, perpendicular to the rod. According to the principles of electromagnetism, specifically Faraday's law of induction, when the rod moves through the magnetic field, a potential difference (emf) is induced across the length of the rod given by the expression emf = Blv, where B is the magnetic field strength, L is the rod's length, and v is the velocity of the rod. Furthermore, the induced current I can be found using Ohm's law, I = emf/R where R is the resistance. The magnetic force on the rod due to this current can be described by the Lorentz force, F = ILB = (Blv/R)LB = B2L2v/R. To move with constant velocity, the applied force must equal the magnetic force but in the opposite direction. Hence, the force the person needs to apply to keep the rod moving at constant velocity is B2L2v/R, making the answer choice (d).