How Do You Calculate the Electric Potential Below a Charged Wire?

AI Thread Summary
To calculate the electric potential below a charged wire, one must consider the charge per length and the distance from the wire's center. The relevant equation involves integrating the charge density over the radial distance. The radius of the wire is significant as it defines the region where the electric field is zero inside the conductor. The potential can be derived by integrating the electric field from the known potential at the surface to the point below the wire. Understanding the relationship between electric field and potential is crucial for solving this problem.
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Homework Statement



One conductor of an overhead electric transmission line is a long aluminum wire 2.40 cm in radius. Suppose that at a particular moment it carries charge per length 1.40 µC/m and is at potential 350 kV. Find the potential 10.9 m below the wire. Ignore the other conductors of the transmission line and assume the electric field is everywhere purely radial.

Homework Equations



i think for this problem you would use the integral of dq/r right?

The Attempt at a Solution



i am not sure how to do this problem. it tells me that it is 10.9 m below the line but it doesn't say where under the wire. would i some how use the 350 kV and get the location under the wire? also i am not sure how the radius of the wire comes in the equation. the ones that i have been doing are rods that have no radius so i am not really sure how to do this problem
 
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Does your textbook or course notes discuss the electric field of a line charge? That would be relevant here.
 
yes but the example that they gave is much simpler and it is just a rod with no radius
 
Okay, good.

The same expression for electric field will be true here, as long as:
  • The distance is taken to the center axis of the transmission line
  • The distance is larger than the radius of the transmission line
(Inside the transmission line, E=0 as for any conductor)
 
oh sorry this is asking for electrical potential though
 
Potential and electric field are related via doing an integral.
 

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