Metal bar on conducdting rod take 2 (didn't post first time)

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A metal bar sliding along parallel rails in a magnetic field will move to the right due to the clockwise current induced by the battery's positive terminal. The challenge lies in determining the current's magnitude, which is influenced by the induced electromotive force (emf) as the bar moves. While the initial assumption may suggest the current is greater than V/R due to increasing electric flux, Lenz's law indicates that the induced current will oppose this change, potentially resulting in a current less than V/R. Understanding the interplay between the induced current and the original current is essential for solving the problem. Proper application of Lenz's law and the right-hand rule will clarify the direction and magnitude of the induced current.
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. Homework Statement

A metal bar is free to slide without friction along two parallel metal rails. The circuit is completed by a battery. (conducting bars are in the x direction, left side of drawing the conducitn bars are connected by a battery, the right side is where the metal bar is) If the ciurcuit is in a unifrom B as shown, which is into the page, in what direction will the bar move. If the rails have zero resistance but the bar has resistance R, will the current be V/R, > V/R, or <V/R (v is from power source).


2. Homework Equations
faraday's law of induction
right hand rule

3. The Attempt at a Solution
well, i know for part a that because the positive part of the battery is up, and that the magnetic field flows into the page, that the current flows in a clockwise direction bc current flows from the pos. terminal of the battery. This thus forces the bar to move to the right, as determined by the right hand rule.

Where i get stuck is determining the current. I know that the magnetic force pushes the bar to the right, which causes an increase in area for hte magentic field, and addditonally the electric flux. When the electric flux increases, so does the induced emf. when the emf increases, so does the current. thus, i would like to say that the current is >V/R.

However, Lenz law continues to pop in my mind. lenz law says that an induced emf czuses the current to flow in a way to oppose the change. thus the current might flow in the opposite direction to oppose such a change and result in the current being <V/r. i need help please, homework is due in 11 hrs. please help
 
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You are going about this the right way. You need to find the magnitude and direction of the induced current. Then, if the currents point in the same direction you can add them, otherwise you should subtract them.

HINT:
Lenz's law states that the magnetic field created by the induced current will point in the direction opposite to the change in the magnetic flux. What direction is this? What direction must the induced current be moving, according to the right hand rule?
 
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