2 Consider a current I = 1 A flowing in the positive y direet ion through a rectan-gular conductor as shown in Figure Q2. The conductor has length L = 4 cm,width a = 1 cm, and height b = 0.1 cm. Suppose that a magnetic field B = Bàpermeates uniformly the conductor, with B = 10 T.

Briefly explain why a potential difference AV = V - V, arises at the equilibrium between the left and right sides of the conductor, as shown in the figure. Starting from J = n, qữa and considering the Lorentz force, derive the force acting on the carriers responsible for the current I function of the relevant parameters a, b, I, B and the carrier density ng: Use such result to demonstrate that the carriers responsible for the current in the metal are negatively charged if the potential difference measured between the left and the right facets of the conductor is positive:deltaV = V - V, > 0. To this end, consider that V- V, is positive if the carriers accumulated on the right side have a negative charge. Suppose that the carriers are electrons ( -1.6x 10-19 C) and thatAV = V,- V, = 22 x 10-6 V. Caleulate the carrier density ngmetal, expressed in units of m .%3Din the Hence or otherwise, suppose that the current I is induced by a generator keeping the potential difference between the input and and output facets (sand S) at a constant value DElta Vt/0=0.002 V what is the resistivity p of the conductor