Electrical field between conductors of the same potential

[pranav p v]

TL;DR

This is a question that appeared in gate EE 2007.
My question is ,is there any mistake in this question?
Question clearly says electric field is produced by the sub conductors of same phase. How does it happen? If the conductors are at different potential then there will be electric field. But here those three conductors are at same potential and how does E produce ?


See the attachment

 

[Tom.G]

No.

Here is a rather poor analogy:
Think of a box full of packing noodles or a balloon full of air. No matter where you look in them or measure pressure, the view and the pressure are the same everywhere.

Now if you look or measure at their boundary, you find things are different. It is this difference of some characteristic that defines a field.

Hope it helps.

Tom

 

[Delta2]

Consider three small spheres of radius $r$ each with charge q, placed at an equilateral triangle. The potential at each sphere is equal to $K_c\frac{q}{r}$ ,so all three spheres are at same potential. Is the electric field in the sides and inside the triangle everywhere zero? I don't think so. Zero is only at the center of the triangle, everywhere else there is some electric field.

 

[pranav p v]

Consider three small spheres of radius $r$ each with charge q, placed at an equilateral triangle. The potential at each sphere is equal to $K_c\frac{q}{r}$ ,so all three spheres are at same potential. Is the electric field in the sides and inside the triangle everywhere zero? I don't think so. Zero is only at the center of the triangle, everywhere else there is some electric field.

If those are charged spheres ,I don't have any confusion.but here those lines are current carrying conductors and at the same potential.
If I keep a test charge near a current carrying conductor will it exert a force?
If I keep a test charge in between two current carrying conductor of different potential then there exist a force on test charge because E is there and it's value is the gradient of potential.

 

[Delta2]

If those are charged spheres ,I don't have any confusion.but here those lines are current carrying conductors and at the same potential.

It doesn't matter if they carry current, we can treat them as charged spheres regarding the potential and the electric field around them. To be more precise I see each cross section of the cylindrical conductor as a charged ring. The charges are the well known surface charges that exist in the surface of current carrying conductors.

The gradient of potential is not zero in the space in between current carrying conductors even though they are at the same potential. The logic behind this is again to treat the conductors as charged spheres or charged rings. Though the charged spheres are at the same potential, there is electric field $\mathbf{E}=-\nabla V$, in the space in between.

 

[Baluncore]

If those are charged spheres ,I don't have any confusion.but here those lines are current carrying conductors and at the same potential.

The conductors are not at the same potential.
Ignore the current. The question is about electric field intensity.

 

[anorlunda]

Just to clarify the question, the 3 conductors are not the 3 phases, they are bundled conductors in the same phase.

https://en.wikipedia.org/wiki/Overhead_power_line#Bundle_conductors
Bundled conductors reduce the voltage gradient in the vicinity of the line. This reduces the possibility of corona discharge.

 

[pranav p v]

It doesn't matter if they carry current, we can treat them as charged spheres regarding the potential and the electric field around them. To be more precise I see each cross section of the cylindrical conductor as a charged ring. The charges are the well known surface charges that exist in the surface of current carrying conductors.

The gradient of potential is not zero in the space in between current carrying conductors even though they are at the same potential. The logic behind this is again to treat the conductors as charged spheres or charged rings. Though the charged spheres are at the same potential, there is electric field $\mathbf{E}=-\nabla V$, in the space in between.

So current carrying conductor produces both Electric Field (due to surface charge) and Magnetic Field?
Then why is surface charge creation happening while current flowing through a conductor?
I think if current flowing through a conductor then electric field will not be produced because there is no net charges.If we consider a portion of conductor, then all incoming charges equal to out going and net be zero.

 

[pranav p v]

The conductors are not at the same potential.
Ignore the current. The question is about electric field intensity.

They are at same potential ( same phase)

 

[Baluncore]

They are at same potential ( same phase)

Then the external corner of the triangle, point Y, will have the greatest electric field gradient.

 

[anorlunda]

Not all of the conductors are at the same distance to the other phases, so their voltages will be almost the same but not exactly the same.

This problem invites the student to overcomplicate, but the solution should be simple. You should not need to know the distance to other phases. You should not need to know the exact potential of each sub conductor. You should not need to know how much the current is (including zero current). To make it simple enough to answer, all those things should not matter.

Consider this:

Consider three small spheres of radius r each with charge q, placed at an equilateral triangle.

But each of the three may have different charges $q_1$, $q_2$, $q_3$. Which choice would your answer be then?

 

[pranav p v]

This problem invites the student to overcomplicate, but the solution should be simple. You should not need to know the distance to other phases. You should not need to know the exact potential of each sub conductor. You should not need to know how much the current is (including zero current). To make it simple enough to answer, all those things should not matter.

I answered that question by considering like spheres of charge located at 3 corners(assumed equal charges on 3 spheres). I ignored everything as you said for the answer.

But how does that electric field produce?How can I solve that question by treated those lines like spheres of stationary charges?

I am simplifying my question by "What is the electric field near by a current carrying conductor"

 

[Delta2]

I am simplifying my question by "What is the electric field near by a current carrying conductor"

In my opinion for DC and low frequency AC current the E-field outside a cylindrical conductor is like the E-field inside a cylindrical capacitor, that is the E-field is in the radial direction , perpendicular to the cylindrical conductor's surface. This radial component is due to the scalar potential, that is $\mathbf{E_r}=-\nabla V$.

If the frequency is higher then there is also a z-component (in the same direction as that of the current of the conductor)of the E-field . This component is due to the vector potential $\mathbf{A}$,$\mathbf{E_z}=-\frac{\partial\mathbf{A}}{\partial t}$.

 

[pranav p v]

In my opinion for DC and low frequency AC current the E-field outside a cylindrical conductor is like the E-field inside a cylindrical capacitor, that is the E-field is in the radial direction , perpendicular to the cylindrical conductor's surface. This radial component is due to the scalar potential, that is $\mathbf{E_r}=-\nabla V$.

If the frequency is higher then there is also a z-component (in the same direction as that of the current of the conductor)of the E-field . This component is due to the vector potential $\mathbf{A}$,$\mathbf{E_z}=-\frac{\partial\mathbf{A}}{\partial t}$.

Ok,so a current carrying conductor produces both Electric Field and magnetic field.If that correct, can I think like as follows?
In a current carrying conductor ,charges ( electrons)are moving with respect to the lab frame.since the length contraction happens ,negative charge per unit length is more than that of positive charge and produce electric field ?

 

[Delta2]

Ok,so a current carrying conductor produces both Electric Field and magnetic field.If that correct, can I think like as follows?
In a current carrying conductor ,charges ( electrons)are moving with respect to the lab frame.since the length contraction happens ,negative charge per unit length is more than that of positive charge and produce electric field ?

Now you decide to throw in relativity into a problem that can be solved using classical pre-relativistic electromagnetism. I will not be able to comment on your thoughts, I am not good in relativity.

 

[pranav p v]

Now you decide to throw in relativity into a problem that can be solved using classical pre-relativistic electromagnetism. I will not be able to comment on your thoughts, I am not good in relativity.

Thanks for the responses

 

[Tom.G]

Another way to consider the problem is that the three conductors form a crude Faraday Shield. And as you may have learned, to paraphrase, All items within a conductive enclosure are at the same potential.

https://en.wikipedia.org/wiki/Faraday_cage

Cheers,
Tom

 

[pranav p v]

In a current carrying conductor ,charges ( electrons)are moving with respect to the lab frame.since the length contraction happens ,negative charge per unit length is more than that of positive charge and produce electric field ?

Here my idea is wrong because the space between those electrons will not be contracted.so net charge will be nullified.

 

[pranav p v]

Another way to consider the problem is that the three conductors form a crude Faraday Shield. And as you may have learned, to paraphrase, All items within a conductive enclosure are at the same potential.

This an approach to solve the problem.But I wish to know the physics behind the electric field.

 

[cnh1995]

As pointed out earlier, I beileve you should consider the three conductors as 3 long cylinders/spheres, all at the same eletric potential. If you consider the speheres to be positively charged, the E-field of each sphere will be radially outward.
If you add the individual E-field contributions from each sphere at the given points, you can see the E-field is maximum at Y.

But I wish to know the physics behind the electric field.

The E-field is because of the surface charges on the conductor.
Look up "Poynting Vector".