$(30$pts$)$Consider the system shown below consisting of a $60$ V battery that is connected to a $12$ resistor $($there is no other resistance in the circuit$).$ Note that a portion of the circuit is completed by a uniform rod $(250-$grams in mass, $50-cm$ long$)$ that is free to slide along the wires it is in contact with $($in other words the rod can slide in the left$/$right direction in the diagram$).$ The entire circuit is then placed in a region where there is a constant $3-$Tesla magnetic field directed into the page. Ignoring any inductive effects:

a$.$ Determine the current traveling through the circuit

b$.$ Determine the magnetic foree exerted on the rod $($magnitude and direction$)$

c$.$ Determine the acceleration of the rod due to the magnetic force