B

Step 1: Understand the working principle of a thermocouple. A thermocouple generates a voltage (thermo e.m.f.) when there is a temperature difference between its two junctions: the hot junction and the cold junction. This voltage is dependent on the materials of the wires and the temperature difference.

Step 2: As the temperature of the hot junction increases, the e.m.f. generated also increases. Initially, at lower temperatures, the relationship between temperature and e.m.f is nearly linear. However, as the temperature increases further, the response becomes non-linear due to the thermoelectric properties of the materials involved.

Step 3: Analyze the options. Option A, which suggests a constant rate of increase, does not correctly describe the actual behavior. Option C suggests an initial rapid increase which diminishes later; this is not the case either. Option D talks about a neutral temperature, which is less relevant to the thermoelectric effect. In contrast, Option B correctly indicates that the increase in e.m.f. starts slowly and then become more rapid at higher temperatures, aligning with the non-linear response observed.

Conclusion: Therefore, the most accurate option is B: Increases slowly in the beginning and more rapidly at higher temperatures.