A conducting rod is pulled horizontally with constant force F= 3.40 N along a set of rails separated by d= 0.260 m. A uniform magnetic field B= 0.500T is directed into the page. There is no friction between the rod and the rails, and the rod moves with constant velocity v= 6.80 m/s.
1. Using Faraday's Law, calculate the induced emf around the loop in the figure that is caused by the changing flux. Assign clockwise to be the positive direction for emf.
2. The emf around the loop causes a current to flow. How large is that current? (Again, use a positive value for clockwise direction.)
EMF = -d Φ/dt
Φ = ∫(B·dA)
The Attempt at a Solution
1. I didn't expect this to work, but I tried to use the formula E = BLv. I plugged in B, d, and v and the answer was wrong.
A hint was given: When the magnetic field is uniform and normal to the plane of the loop, then the flux is of the product of the field and the area. In this problem it is the area that changes with time, not the field.
Even with the hint I'm still confused. Since area is changing with time, how do I incorporate that into my calculation?
2. I first tried using F = IL x B to solve for I but it was wrong. The hint said Remember F=ma: since v is constant, a=0, so it must be true that the net force on the rod is zero. The pulling force is compensating the force on the rod due to the current through it and the magnetic field.
So what does this mean? I'm so confused on what to do.
Any help is appreciated!