How Should Electric Potential Energy Be Ranked at Point P?

[STEMucator]

Homework Statement

Rank the electric potential energy at point $P$ for the following four cases:

http://gyazo.com/c7d9df3d3d64cda909ddc0d2ab7686bc

Homework Equations

$\Delta U_e = - W_∞$

The Attempt at a Solution

I believe it should be $U_2 > U_1 > U_3 > U_4$, but I am not certain.

 

[ehild]

Why do you think what you believe? How is electric potential defined? And what is the electric potential at distance r from a point charge q?

ehild

 

[STEMucator]

Why do you think what you believe? How is electric potential defined? And what is the electric potential at distance r from a point charge q?

ehild

Ah I see, so $V = k \frac{q}{r}$ in combination with $V = \frac{U_e}{q}$.

This yields $U_2 > U_1 = U_3 = U_4$.

Thank you.

 

[ehild]

Ah I see, so $V = k \frac{q}{r}$ in combination with $V = \frac{U_e}{q}$.

This yields $U_2 > U_1 = U_3 = U_4$.

Thank you.

The solution is correct now.

Yes, the potential is the potential energy of a unit positive charge at a certain point of the electric field. It is defined with the work done by the field:
The potential at a point P is equal to the work done by the electric field on a unit positive charge while it moves from P to the place where the potential is zero.

You know from Gauss Law that the electric field around a charge q is E=kq/r². It is a conservative field. The potential U(r_P) is the work on a unit positive charge when it moves from r_P to infinity: $$U(r_P)=W\big |_{r_P}^{\infty}=\int _{r_P}^{\infty}{\frac{kq}{r^2}dr}=k\frac{q}{r_P}$$.

ehild