Question

Suppose you have two point charges of opposite sign. As you move them farther and farther apart, the potential energy of this system relative to infinity increases? decrease? or stays the same?

Answer 1

Answer:

Potential energy of the system increases relative to infinity.

Explanation:

Potential energy of two point charge is defined as,

$U=\frac{q_{1}q_{2} }{4\pi\epsilon_{0}r^{2}}$

Here, $q_{1}and q_{2}$ are two point charge, r is the distyance between the two charges.

Now according to the question charge is of equal magnitude but opposite sign.

Therefore potential energy,

$U=\frac{q(-q) }{4\pi\epsilon_{0}r^{2}}\\U=- \frac{q^{2} }{4\pi\epsilon_{0}r^{2}}$

From the above formula if the distance increases then magnitude of potential energy decreases.

And due to presence of negative charge magnitude of Potential energy is increases with increasing distance.

Therefore, the potential energy is increasing if we move two opposite charge farther.

Answer 2

When we have two point charges of opposite sign, as we move them farther and farther apart, the potential energy of this system relative to infinity will : increases

when 2 point charges of opposite sign, it will started out as negative. It will got closer and closer to zero as the particles move apart

hope this helps