Is u=qv or u=0.5qv the correct equation for finding potential energy?

[sonutulsiani]

Homework Statement

Ok I am really confused!
Sometimes we use u=qv to find the potential energy
and sometimes u=0.5qv
Which one is correct?

Homework Equations

u= electro static potential energy
v= voltage
q is charge

The Attempt at a Solution

 

[nickjer]

That question is very vague. You will have to be more specific of the problem.

U=qV is used for a charge (q) in an electrostatic potential (V). "U" is then the electric potential energy the charge has in that field.

I am not sure about U= 0.5qV, since that is very vague. If you can give an example where it is used, then you might be able to narrow it down.

 

[sonutulsiani]

like for energy in a capacitor its used

 

[nickjer]

The energy stored in a capacitor is very different than a single point charge in an electric field. The energy stored in a capacitor is actually an integral over many infinitesmal point charges, dq. Since it is a sum, you can't expect it to look like qV.

 

[sonutulsiani]

Apparently my textbook writes potential energy of 2 point charges is u=qv
and electrostatic potential energy is u=1/2qv. What is the difference between them other than the word 'electrostatic'

 

[nickjer]

Electrostatic just means the electric field isn't changing with time. So you can use it interchangeably with electric for most of your cases. You can say the electrostatic potential energy of 2 point charges is U = qV, since there is no time dependence that would cause magnetic fields.

For your U = 1/2 qV, you must be reading about capacitance and the stored energy in the electric field of the charges. They are both different, and shouldn't get them too confused from a question you might be asked.

 

[Alihammoud]

u = q v is for electrical potential energy
for those who gave the example of capacitors:
u = 0.5 c v^2

 

[lepton5]

Homework Statement

Ok I am really confused!
Sometimes we use u=qv to find the potential energy
and sometimes u=0.5qv
Which one is correct?

I will try to sharp two eqn above based on common textbook,

1) $$W = q . [V(a) - V(b)]$$

this eqn tells us for the work done to move a charge from point (a) to point (b). V here means potential difference between points (a) and (b).

2) $$W = \frac{1}{2}\Sigma^{n}_{i=1} q_i V(r_i)$$

this eqn tells about work it takes to assemble a configuration of point charge. so W here represents energy stored in the configuration. factor 1/2 here is used to restore the eqn that initially count twice. (if you confused what I mean, you can check for yourself the derivation of this eqn). this eqn is more about the energy of a point charge distribution.