(Solved): Problem 1: Magnetic Force (10 pts.) A copper rod of mass m and length L is hung from the ceiling us ...

Problem 1: Magnetic Force (10 pts.) A copper rod of mass $\mathbf{m}$ and length $\mathbf{L}$ is hung from the ceiling using two springs of spring constant $\mathbf{k}$. A uniform magnetic field of magnitude ${\mathbf{B}}_0$ pointing perpendicular to the rod and spring (going into the page in the figure) exists in a region of space covering a length $w$ of the copper rod. The ends of the rod are then connected by flexible copper wire across the terminals of a battery of voltage $\mathbf{V}$. (Ignore any force by the flexible wire.) When a current $\mathbf{I}$ through the copper rod in the direction shown in figure is turned on: A. what is the change in the length of the springs? (8 pts.) B. what direction does the rod move? (2 pts.)