# Why when two conductors connected by a conducting wire gain the same potential . ?

Why when two charged conductors connected by a conducting wire gain the same potential .
Lets say we have two spheres of different charges why when we connect them by a single copper wire they gain the same potential
Thanks in advance

## Answers and Replies

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tiny-tim
Science Advisor
Homework Helper
hi nishantve1!

tell us what you think, and then we'll comment!

I am new to Electrostatics , first of all I have no idea but still what I am able to figure out is maybe the charges on both become equal but I see thats not much to do with the potential or is it am I right ?

tiny-tim
Science Advisor
Homework Helper
I am new to Electrostatics …
ok, well, always start with the definitions, then write out all the equations you know, and see if any of them help …

(btw, that is why the pf homework template requires you to write out the equations first, and please post in the homework sub-forum in future)

DEFINITION:

what is electric potential?

what does it do?​

EQUATIONS:

what equations do you know for electric potential?​

Sorry , next time I will definitely post in homework sub forum

Electric potential I know is Work done per charge in bringing it from infinity to a point .
Electric potential is Like gravitational potential it The closer a test charge is to a electric field source more potential energy it has and thus more Electric potential .
Electrons flow from higher to lower potential thats what makes electricity flow

V(a) - V(b) = integral from a to b E.dl

E = -dV/dr

V = E.d

Due to a point charge at a distance R the electric potential is Q/4 pi Epsilno0 R

tiny-tim
Science Advisor
Homework Helper
Electric potential I know is Work done per charge in bringing it from infinity to a point .
mmm … that's only if the potential defined to be zero at infinity (in electric circuits, it usually isn't )

better is to talk about potential difference

electric potential difference

= potential energy difference per charge

= minus work done, per charge, by the electric field
Electrons flow from higher to lower potential …
i always get confused about this , but isn't that for positive charge?
Why when two charged conductors connected by a conducting wire gain the same potential .
Lets say we have two spheres of different charges why when we connect them by a single copper wire they gain the same potential
ok , now call the potentials V and W, and apply the above to how an individual charge will move, and how that will affect the potential difference

oh yeah electrons flow form lower to higher potential .if both the bodies have charge of same polarity say Positive then electrons from one with lower potential say W will flow to one with higher potential V . now what ? the electrons will go and neutralize the positive charge on the other one . And if there polarities were to be different then electrons will flow the same way as above . I am seriously not able to figure out please Help me !

tiny-tim
Science Advisor
Homework Helper
you're more or less there

the information you haven't yet used is that there's only a fixed amount of total charge

(i assume the spheres are isolated, ie not connected to any voltage source)

so if the total charge is fixed, what's going to happen?

Ok so lets name the spheres there is Sphere A with four Positive charges (just keeping things simple) and is at a higher Potential and the another sphere B has one Positive charge and is at a lower potential .
{That means the work done per charge on Bringing a test charge from a Point where we assume U to be 0 will be higher in case of A }

Now we connect them by a conducting wire , so the electrons from A will want to flow to B . and since the charge is conserved we have only 5 positive charges in the system .
Now what the charges on A and B could be like
5 0
6 -1
7 -2
8 -3

and similarly many keeping the charge +5 constant What happens then

Hi. Say two charged conductors of charge +Q, -Q form condenser of electrostatic capacity C. So, potential difference is V=Q/C.
WHY: By current in connecting wire Q decrease so V also decrease.
WHEN: When Q=0, V=0 same potential.
Regards.

I have also learnt that if there are two bodies(with similar characteristics) with charges Q1 and Q2 if they are brought in contact the charges gets distributed like (Q1 + Q2)/2 . Is that the case here

Hi. Say two charged conductors of charge +Q, -Q form condenser of electrostatic capacity C. So, potential difference is V=Q/C.
WHY: By current in connecting wire Q decrease so V also decrease.
WHEN: When Q=0, V=0 same potential.
Regards.
I get what you are trying to say . but how does charge Q becomes 0 ?

tiny-tim
Science Advisor
Homework Helper
Now we connect them by a conducting wire , so the electrons from A will want to flow to B . and since the charge is conserved we have only 5 positive charges in the system .
Now what the charges on A and B could be like
5 0
6 -1
7 -2
8 -3

and similarly many keeping the charge +5 constant What happens then
… if there are two bodies(with similar characteristics) with charges Q1 and Q2 if they are brought in contact the charges gets distributed like (Q1 + Q2)/2 . Is that the case here
that's right!

so it'll go (it's easier with an even number )
6 0
5 1
4 2
3 3​

sooo … when the charges are equal, what is the potential difference (and why?)

6 0
5 1
4 2
3 3 [/INDENT]

sooo … when the charges are equal, what is the potential difference (and why?)
When the charges are equal this means that they are at the same potential . So the potential Difference will be zero . Its very easy to understand that Equal charges are at the same potential . Is it like the Potential Energy required in bringing that charge from infinity to a point in space is same for the other charge since they are equal in magnitude . Is there any Mathematical Equation that proves it I mean I tried using

V(a) - V(b) = Integral from A to B E.dr

which should be zero but how ?

tiny-tim
Science Advisor
Homework Helper
ooops!

i thought these were identical spheres, but looking back, they're not

so … correction … the charges won't equalise, although the potentials will equalise

so the question should be, why will the electrons keep moving while the potential difference is non-zero, and stop moving when the potential difference is zero?

Hi.
so the question should be, why will the electrons keep moving while the potential difference is non-zero, and stop moving when the potential difference is zero?
You say Why Ohm's law V=RI.
Regards.

Hi.
. but how does charge Q becomes 0 ?
Cancel of Q in positive charge plate and -Q in negative charge plate. Total discharge of battery.
Regards.

I am still in Capacitance so No idea about Ohm's law . Also its almost time I have to go to school . If someone please please explain it I will be very thankful . Also if potential difference is zero why will electrons move ? If I am still not Familiar with current Electricity is this question out of the scope ?

@sweet springs I got that but what if both charges were of same polarity and different magnitude ?