Electric potential of a conducting rod in a homogen. electric field

[antel-x]

Hello,
I have puzzled myself with a question: what is the potential of a conducting rod in a homogeneous electric field (net rod charge = 0)? To be more exact I imagine a conducting rod suspended on a non-conducting thread in the Earth electric field near and perpendicular to its surface. If the rod is in contact with the the Earth then its potential is the ground potential. What confuses me is that a conductor is in contact with variable potentials across its length but the rod must have only one certain value due to charge balance. Any help is very appreciated.

 

[tiny-tim]

welcome to pf!

hello antel-x! welcome to pf!

… a conductor is in contact with variable potentials across its length …

i don't understand this …

if it's in contact with different potentials (btw, why would it be? ), then a current will flow along it

 

[antel-x]

our planet is a big capacitor. there's a potential drop of about 130 V/m. therefore a conducting rod hanging perpendicular to the ground experiences a change of potential along its length. i am aware that a charge separation within a rod would take place with electrons collected near the higher end. the question is what is the potential of the rod?

 

[tiny-tim]

hi antel-x!

(just got up :zzz:)

our planet is a big capacitor. there's a potential drop of about 130 V/m. therefore a conducting rod hanging perpendicular to the ground experiences a change of potential along its length. i am aware that a charge separation within a rod would take place with electrons collected near the higher end. the question is what is the potential of the rod?

ah i see

yes, the Earth has a surprisingly high electric field, which various sources give as between 130 and 170 V/m (N/C)

a vertical rod will therefore have a tiny charge at the end

from a 1974 "scientific america" article by c l strong (http://www.only1egg-productions.org/AltSci/ElectrostaticMotors/electrostatic_motors.htm) …

The field exists in the atmosphere between the Earth's surface and the ionosphere as an electric potential of about 360,000 volts.
…
The energy of the field can be tapped with a simple antenna in the form of a vertical wire that carries one sharp point or more at its upper end. During fair weather the antenna will pick up potential at the rate of about 100 volts for each meter of height between the points and the Earth's surface up to a few hundred feet. At higher altitudes the rate decreases. During local thunderstorms the pickup can amount to thousands of volts per foot.
…
Why not tap the field to supplement conventional energy resources? Several limitations must first be overcome. For example, a single sharp point can draw electric current from the surrounding air at a rate of only about a millionth of an ampere. An antenna consisting of a single point at the top of a 60-foot wire could be expected to deliver about a microampere at 2,000 volts; the rate is equivalent to .002 watt. A point-studded balloon tethered by a wire at an altitude of 75 meters might be expected to deliver .075 watt. A serious limitation appears as the altitude of the antenna exceeds about 200 meters. The correspondingly higher voltages become difficult to confine.​

… I imagine a conducting rod suspended on a non-conducting thread in the Earth electric field near and perpendicular to its surface … the rod must have only one certain value due to charge balance. Any help is very appreciated.

yes the rod is a conductor, so (in equilibrium) the charge in the rod rearranges itself (on the surface) so as to cancel out the external (earth's) electric field inside the rod

this rearrangement only requires a few electrons at the end of the rod (and the power involved is so small that we don't notice it)

the whole interior of the rod is then at the same potential, and the field immediately outside the rod is slightly distorted by the rearranged charge on the rod

 

[antel-x]

thank you for the very extended reply. you said in your final lines: "at the same potential" which is ... i suppose is non-zero with respect to ground. however the potential drop across the rod is 0 as electric field gradient from the Earth's field is canceled by the electric field established by separated charge on the rod surface.

 

[tiny-tim]

hi antel-x!

yes, the potential drop across the rod is 0