4. A copper rod of mass m rests on two horizontal rails a distance d apart, and carries a current io from one rail to the other. The coefficient of statie friction is u. A uniform magnotic field of unknown magnitude B points upward at angle 0. Here is a side view: a) The magnetic force on the wire has not been included in the above diagram. What is the magnitude of this force? Sketch the force vector on the diagram, and break it into horizontal and vertical components. b) If the wire is just on the verge of aliding sideways, then how large is the magnetic field B? Your answer will involve 0. B N c) By minimizing your expression for B with respect to 0, find the smallest magnetic field that could cause the wire to slide sideways. d) If the magnetic field were vertical, which direction would the force on the wire point? Why is the optimal magnetic field found in part (c) not vertical? mg In this diagram, the current in in the wire is coming out of the page, and f denotes the friction force. Notice that the magnetic field vector B is not a force vector.

4. A copper rod of mass m rests on two horizontal rails a distance d apart, and carries a current io from one rail to the other. The coefficient of statie friction is u. A uniform magnotic field of unknown magnitude B points upward at angle 0. Here is a side view: a) The magnetic force on the wire has not been included in the above diagram. What is the magnitude of this force? Sketch the force vector on the diagram, and break it into horizontal and vertical components. b) If the wire is just on the verge of aliding sideways, then how large is the magnetic field B? Your answer will involve 0. B N c) By minimizing your expression for B with respect to 0, find the smallest magnetic field that could cause the wire to slide sideways. d) If the magnetic field were vertical, which direction would the force on the wire point? Why is the optimal magnetic field found in part (c) not vertical? mg In this diagram, the current in in the wire is coming out of the page, and f denotes the friction force. Notice that the magnetic field vector B is not a force vector.