$(24$ Points$)$ A conducting rod that has a mass $m$ and a negligible resistance slides along two parallel rails that have negligible resistances and are separated by a distance $l$ and connected by a resistance R $.$ The coefficient of kinetic friction between the rod and the rails is ${}_k.$ The rails are attached to an inclined plane that makes an angle $$ with the horizontal. There is a magnetic field directed upward as shown.

a$.$ Find an expression for the normal force acting on the rod in terms of $B,v,R,l,{}_k,$ and $.$

b$.$ Find an expression for the magnetic force acting on the rod in terms of $B,v,R,l,{}_k,$ and $.$

c$.$ Find an expression for the force of kinetic friction acting on the rod in terms of $B,v,R,l,{}_k,$ and $.$

d$.$ Find an expression for the terminal speed of the rod in terms of $B,v,R,l,{}_k,$ and $.$

Physics $250$B

Page $2$