Charging a system of metal rods

[rijulg]

I am trying to charge a system of two metal rods, of definite length, placed a certain distance apart. But before setting up the rods and hooking them to any battery, i wish to know the magnitude of charge that will be accumulated on the rods and what is the maximum possible charge on the rods, so as to just prevent electrical discharge

 

[rijulg]

we know that field of a charged rod (infinite, or finite near center) is ~ E= λ/(2πϵr), and maximum possible electric field is 3 x 10^6 N/C, so putting the values we get relation between λ and r, knowing length of rod, we can calculate maximum charge on one rod with respect to radius of cross section of rod. But i doubt the applicability and validity of this method

 

[jtbell]

But i doubt the applicability and validity of this method

Why?

 

[rijulg]

Why?

because this approximation is for infinite charge rod, and for a finite charge rod, the field might be more on the axis, so when i will charge my rod according to calculations of infinite rod, it may discharge from the axis

 

[jtbell]

Ah, I overlooked the "definite length" in your first post. It seems you want the electric field at all points near a cylinder with given length. This is not a simple problem, even if the cylinder has a circular cross-section (the most symmetric situation) and the charge is uniform. The field does not have the same strength or direction everywhere on the surface. It's not like an infinite circular cylinder where you can assume the field is perpendicular to the surface of the cylinder.

Also, you're using conducting (metal) rods, which means the charge is not uniformly distributed. It's all at the surface of the rods, and with probably a higher (surface) charge density near the ends of the rod.

I think you have to solve Laplace's equation numerically for the electric potential, with the condition that the surfaces of the rods are equipotentials, then find the electric field by taking the gradient of the potential. Maybe someone else has a better idea.

 

[rijulg]

Ah, I overlooked the "definite length" in your first post. It seems you want the electric field at all points near a cylinder with given length. This is not a simple problem, even if the cylinder has a circular cross-section (the most symmetric situation) and the charge is uniform. The field does not have the same strength or direction everywhere on the surface. It's not like an infinite circular cylinder where you can assume the field is perpendicular to the surface of the cylinder.

Also, you're using conducting (metal) rods, which means the charge is not uniformly distributed. It's all at the surface of the rods, and with probably a higher (surface) charge density near the ends of the rod.

I think you have to solve Laplace's equation numerically for the electric potential, with the condition that the surfaces of the rods are equipotentials, then find the electric field by taking the gradient of the potential. Maybe someone else has a better idea.

Actually i need very less out of the problem, i just need to find out the maximum amount of charge possible on the rod, even a rough estimate and then i will charge it with somewhat lesser charge than the acquired answer, but to find out that rough estimate i am not sure if infinite rod estimation will be of any actual use, if someone can even just give a way to find out an assuring approximation of max. charge so that i can start building a model, it would be great