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(c) A vector potential A in cylindrical coordinate (f, 0, 2) is given as
Ã = ( cos e
-)f -r sin tê
Find the expression for the current density that will produce the above
vector potential in the free space.

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Let us we consider two resistors in series, both with the same dimensions, and the same effective mass. The first resistor has a scattering rate t, and the second has a scattering rate of t71. They both have area A and length L and the same charge density and effective masses. (i) Calculate the total resistance, then by treating the total resistance of the circuit as a resistor of length L, area A, show that the total scattering rate for the combined circuit, t' can be written as t, = t1 +t7. If t1=100 Terahertz, and t,1=AT where A=0.3 Terahertz/Kelvin and T is the temperature, assuming that n, e and m* remain constant, sketch the dependence of the conductivity on the temperature. If the fermi energy is 12 eV and the effective mass is 0.4me what is the conductivity at room temperature (303 K)? (ii) (iii)