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

[nishantve1]

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

 

[tiny-tim]

hi nishantve1!

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

 

[nishantve1]

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 that's not much to do with the potential or is it am I right ?

 

[tiny-tim]

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?​

 

[nishantve1]

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 that's 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]

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

 

[nishantve1]

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]

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?

 

[nishantve1]

Ok so let's 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

 

[sweet springs]

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.

 

[nishantve1]

I have also learned 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

 

[nishantve1]

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]

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?)

 

[nishantve1]

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]

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? ​

 

[sweet springs]

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.

 

[sweet springs]

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.

 

[nishantve1]

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 ?