Question

# Consider a current I = 1 A flowing in the positive y direction 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 deltaV = V - V, arises at the equilibrium between the left and right sides of the conductor, as shown in the figure. Starting from J = ng 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, 1, B and the carrier density ng-such result to demonstrate that the carriers responsible for the current I in the metal are negatively charged if the potential difference measured between the left and the right facets of the conductor is positive:delta V = V - V, > 0. To this end, consider that V - V, is positive if the carriers accumulated on the right side have a negative charge.Use Suppose that the carriers are electrons (. -1.6 x 10-19 C) and that deltaV = V – V, = 22 x 10-6 V. Calculate the carrier density n, in the metal, expressed in units of m . Hence or otherwise, suppose that the current I is induced by a generator keeping the potential difference between the input and output facets (Sin and Sout) at a constant value delta v =0.002v what is the resistivity p ogf the conductor( in ohms)

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