![]() (a) Construct a cylindrical Gaussian surface perpendicular to the charge sheet as shown:Ī Qs E The cross-sectional area is A. If one defines the potential to be zero at infinity. Since E =−dV/dr, the electric potential at a point on the sphere is V= Where E is the magnitude of the electric field on S. ![]() By symmetry, the electric field at every point on S has the same magnitude and points outward perpendicular to the surface. With the point charge Q at the center, construct a closed spherical surface S with radius r. For shallow donors with low to moderate concentration at room temperature, (Nd/Nc)exp Ec. Here only the positive root has been kept. ![]() Treating exp(Ef/kT) as an unknown, the above equation is a quadratic equation with the solution 1 eΔE / kT =, 1 + e− ΔE / kT eΔE / kT + 1Īdding the above two equations yields f ( E f − ΔE ) + f ( E f + ΔE ) =
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