Final answer:
The induced emf in a conducting rod moving through a magnetic field is calculated using the product of magnetic field strength, rod length, and velocity. The resulting current and power dissipation are determined by Ohm's Law and the power equation. The external agent's work rate equates to the force necessary to maintain the rod's velocity times that velocity.
Step-by-step explanation:
A conducting rod moving through a magnetic field experiences an induced emf, which can be calculated using the formula emf = B × L × v. Lenz's Law, and the right-hand rule helps determine the direction of the induced current. The physics concepts involved relate to Faraday's Law of Induction, the generation of motional emf, and power dissipated in the form of thermal energy in a resistor.
Calculations for induced EMF, Current, and Power
The induced emf in the rod is simply the product of the magnetic field (B), length of the rod (L), and velocity (v), which goes as follows: emf = 1.2 T × 0.1 m × 5.0 m/s = 0.6 V. Given the resistance of the rod (R = 0.4Ω), the current can be calculated by Ohm’s law: I = emf/R, which yields I = 0.6 V / 0.4Ω = 1.5 A. The rate at which thermal energy is being generated in the rod (Power) can be found using P = I²R, resulting in P = (1.5 A)² × 0.4Ω = 0.9 W. To maintain the constant velocity, the external agent's applied force should counteract the magnetic drag, resulting in a force that equals the product of current, magnetic field, and length of the rod, F = I × B × L. Finally, the work done by the force per unit time (power), is given by the product of the velocity and the force.