Why is the electric potential at infinity zero?

Question

As per net results, the potential at infinity is considered to be zero. Apart from considering this as a physics law, is there any proper reason why we consider potential at infinity to be zero?

Answer 1

By definition the potential energy is chosen to be zero at infinity. It can also be defined to be zero at the ground. Generally speaking the work $W$ done for moving a body against a force $\vec F(\vec r)$ from point $A$ to $B$ is given by the difference of potential energies $$ W = U(\vec r_A) - U(\vec r_B). $$ That is to say the potential energy at point $B$ is $$ U(\vec r_B) = U(\vec r_A) - \int_{\vec r_A}^{\vec r_B}\vec F(\vec r)\cdot d\vec r\,. $$ As we can see, we can choose our reference point $\vec r_A$ and potential energy there $U(\vec r_A)$ arbitrarily since it cancels out with the integral.

Answer 2

Because any function that drops off as $1/r$ asymptotically approaches $0$.

Answer 3

According to me potential energy is based on the interaction between two objects. Take for example gravitational potential energy which is a result of interaction of the body with the gravitational field of earth.

Since at infinity, interaction between two objects is negligible, therefore the potential energy is considered to be 0 there.

Answer 4

This is not always correct. For sources extending to infinity, the potential is not 0 at infinity! This holds for localized sources only. For localized sources, we are free to set any value at infinity and hence can be taken equal to 0. However, for sources extending to infinity, we can't choose arbitrary values at infinity since the source is also "present" there.