Question

Question 2. A conducting bar moves rightward with a constant velocity v on two conducting parallel rails. The two conducting parallel rails are separated by a distance d. The two conducting parallel rails are connected with a resistor R. The setup is located in a uniform magmatic field B out of page. Bu Please show all steps and explain every step in your own words. 1) If there is an induced current in the loop, which direction is it and why? Explain how you analyze the change and find the direction of the induced current step by step. (5 points) 2) Find the magnitude of the induced emf in the loop. (5 points) 3) Find the induced current in the loop. (2 points) 4) Find the direction and magnitude of the magnetic force acting on the moving bar. (3 points) 5) If the speed doubles, how does the power consumed in the circuit change and why? (5 points) 6) Bonus question: What provides the electric energy consumed in the circuit? Explain in your own words. (5 points)

Answer 1

1. Yes, there will be an induced current in the loop. SInce its a metallic bar that moves towards right in a Magnetic field, it will have charges inside it, free to move. Since cahrges moving through a magnetic field feel a force, Lorentz force given by F= q.v.b.Sin(90). So the electrons which are free to move, will be pushed by this force, whose direction can be found from RIght Hand Thumb Rule. Applying RIght Hand Rule here, with Magnetic Field coming out of page, and velocity in Right direction, we get that the electrons feel a downwards foce in the bar.

Eventually, enough of them will be at the bottom of the bar, that there will also be a net positive charge at the top, thus inducing an electric field within the bar, which balances the Magnetic field, ultimately reaching an Equilibirim.

Note that we will have to continously keep the bar moving to keep the emg going.

But due to the separation of charges, there is an induced current in the loop, opposite to the direction of flow of electrons, ie Counter Clockwise.

2. At the equilibirum, the Magnetic force is balanced out be electric force, giving FB=FE

Thus q.v.B = q.E

Thus E=v.B

Now potential difference is = E.d where d is distance between charges equal to length of rod.

Thus induced emf = v.B.d

3. The current induced in the bar can be found from Ohm's law, where V=IR

Thus i= V/R= v.B.d/R

4. Force on the bar is given by F=i.d.B Sin 90 Given by Forentz Force Law.

Thus F= v.B.d.d.B/R = vB2d2/R