Question

What would be the consequence of setting the potential at \(+100 \mathrm{~V}\) at infinity, rather than taking it to be zero there? a) Nothing; the field and the potential would have the same values at every finite point. b) The electric potential would become infinite at every finite point, and the electric field could not be defined. c) The electric potential everywhere would be \(100 \mathrm{~V}\) higher, and the electric field would be the same. d) It would depend on the situation. For example, the potential due to a positive point charge would drop off more slowly with distance, so the magnitude of the electric field would be less.

Short answer

Answer: The consequence of setting the electric potential at infinity to +100 V is that the electric potential at every finite point will be 100 V higher, while the electric field remains the same.

Step-by-step solution

Checking option a)

The first option proposes that changing the potential at infinity to +100 V would have no effect on the electric field or potential at every finite point. This looks contradictory, since the potential is directly related to the electric field, so it can't remain unaffected when the reference point is changed. Therefore, option a) is not correct.

Checking option b)

The second option suggests that if we set the potential at infinity to +100 V, the electric potential would become infinite at every finite point, and the electric field could not be defined. This statement seems unrealistic because the electric field would still exist, in spite of changing the reference point of the potential. Thus, option b) is not correct either.

Checking option c)

The third option says that changing the potential at infinity would cause the electric potential everywhere to be 100 V higher, while the electric field would remain the same. Indeed, setting the potential to +100 V at infinity would shift the reference point, but this shift will not alter the electric field since it only depends on the position of charges and their magnitudes. Consequently, option c) seems the most logical, and we accept option c) as the correct answer.

Checking option d) for understanding

The last option suggests that the result of setting the potential at infinity to +100V would depend on the situation. However, this is not the case, as it will only shift the reference point without affecting the electric field. Therefore, option d) is incorrect. In conclusion, modifying the reference point for potential at infinity to +100 V only affects the potential's value by adding 100 V everywhere, while the electric field remains unchanged. Therefore, the correct answer is option c).