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A simple model of intrinsic stochastic electromagnetic fields and a simple transmission line model are combined to analytically derive closed-form expressions for the average field coupling to a transmission line. The results are valid under the assumptions of transmission line theory for a line with general load resistances. The theoretical analysis starts with the calculation of the mean squared current magnitude along the line and at the ends. This result is transferred to the coupled voltage. Then, the characteristics of the statistic distribution can be used to calculate other important parameters like the variance or the maximum value.