Why is potential energy at infinity zero when force at infinity is zero? In case of electrostatics and electrodynamics, we can derive that force and potential energy at infinity is zero. However if we only know force at infinity is zero, then how can we derive from this fact that potential energy at infinite is also zero?
 A: The electrostatic potential is zero at infinity because we define it that way; this result is not 'derived' from anything else. You can add any arbitrary constant to the potential, if you find it convenient, and it will be equally valid - but it will no longer be zero at infinity. The only reason we choose it to be zero at infinity is because it's convenient - nothing less, nothing more.
A: If two objects are separated by infinity, then they cannot interact, because electromagnetic force will never reach opposite side, thus potential energy is zero, even if electromagnetic force is not zero.
A: It does not matter. what matters is the difference of potential energy, you can assume an arbitrary constant but it will cancel out when we take their difference 
Let at point $A$ potential energy be $Ua+P$ and at point $B$ potential energy be $Ub+P$. Now their difference will be simply $Ua-Ub$ 
A: look at it this way , we have defined potential difference as the work done per unit charge.
work done can or can not be path dependent
suppose point A is a point near you and a point B is at a infinite distance from A
point B is at r= infinite distance from A
potential varies 1/r  so for r=infinite
1/r turns zero
potential at B some= constant * 1/r  = 0 only
