How do I solve this?

1.

Twelve identical resistors R are connected together to form a cube. In other words, there is one resistor on each of the 12 edges of a cube and at each of the 8 corners of the cube three resistors are connected together. See the gure below. A current I is injected into corner A and withdrawn from comer B (which lies furthest away from A, along a body diagonal passing through the center of the cube). (a) [4]What is the resistance of this cubical an'angement, as measured between the current injection and withdrawal points? (b) [2] What is the voltage difference between the injection and withdrawal points, A and B, assuming the current is 1A and R=l Ohm? (c) [4] What is the voltage difference between points C and D shown in the figure given the numbers in (b)? Hint: Use the symmetry in the problem, either to find out what current flows in each link, or to identify same-voltage points. A metallic rod is lying on a track made of a center rail and two outside rails. Also, in between the outside rails and a middle rail there is a magnet providing a eld of B=1T (out of the page) on y>0, and B=1T (pointing into the page) y