What Is the Potential of an Uncharged Conductor Near a Charged Conductor?

[Tanishq Nandan]

Homework Statement

Consider a finite,uncharged,insulated conductor placed near a finite positively charged conductor.The uncharged body must have a potential
A)less than the charged conductor and more than at infinity
B)more than the charged conductor and less than at infinity
C)more than the charged conductor and more than at infinity
D)less than the charged conductor and less than at infinity

Homework Equations

None,theoretical question..

The Attempt at a Solution

I just took a case of two spherical capacitors,first one being uncharged and second one charged (say positively charged).If the second sphere is brought near the first one,it induces a negative charge on one side of the sphere and a corresponding positive charge on the other side of the sphere.The charge distribution may not be uniform,but is is such that the field inside the conductor becomes zero.
Now,if we calculate the potential of the sphere,it will still turn out to be zero,right?
(K × total charge/common distance)...and the potential at infinity is zero as well..hence,my problem.

 

[ehild]

Homework Statement

Consider a finite,uncharged,insulated conductor placed near a finite positively charged conductor.The uncharged body must have a potential
A)less than the charged conductor and more than at infinity
B)more than the charged conductor and less than at infinity
C)more than the charged conductor and more than at infinity
D)less than the charged conductor and less than at infinity

Homework Equations

None,theoretical question..

The Attempt at a Solution

I just took a case of two spherical capacitors,first one being uncharged and second one charged (say positively charged).If the second sphere is brought near the first one,it induces a negative charge on one side of the sphere and a corresponding positive charge on the other side of the sphere.The charge distribution may not be uniform,but is is such that the field inside the conductor becomes zero.
Now,if we calculate the potential of the sphere,it will still turn out to be zero,right?
(K × total charge/common distance)...and the potential at infinity is zero as well..hence,my problem.

Zero field means constant potential, not necessarily zero. What do you know about the potential on a metal body?
Think how the electric field and potential vary far from the two spheres. Is the potential positive, can it increase with distance somewhere?

 

[Tanishq Nandan]

Well,yeah,once the distance from the centre is greater than the radius,it acts as a point charge,and the field decreases with distance

 

[ehild]

Well,yeah,once the distance from the centre is greater than the radius,it acts as a point charge,and the field decreases with distance

Yes, near the conductors, the field is distorted, but far away, it is like the one of a point charge.
The arrows show the field lines in the figure. What do you think, is the uncharged (gray ) body at positive or negative potential with respect to infinity? Is it at lower or higher potential than the positively charged body?

 

[Tanishq Nandan]

Ok,got it..
For the gray body,the charged conductor will act as a point charge and impart some potential to it..
KQ/d which is going to be lesser than KQ/R (R is radius of charged conductor),
as R is obviously smaller than d...but,the potential is still positive,so it's greater than the potential at infinity..
That would mean option A.
Correct??

 

[ehild]

Ok,got it..
For the gray body,the charged conductor will act as a point charge and impart some potential to it..
KQ/d which is going to be lesser than KQ/R (R is radius of charged conductor),
as R is obviously smaller than d...but,the potential is still positive,so it's greater than the potential at infinity..
That would mean option A.
Correct??

Looks good.
The potential decreases in the direction of the electric field, so it is higher at finite length than at infinity.
The positively charged body induces some negative charge on the closer surface of the neutral body, and some field lines connect some positive charge with the negative charges between the bodies; so the potential decreases from the charged body to the neutral one.