Physical Science Problem?
Consider a very long insulating wire, which is coated with a uniform linear charge density (charge per length) λ. (a)Consider a segment of the wire very far from any endpoints. In which direction does the electric field point?
(b)What is the magnitude of the electric field at any point a distance r from the wire? (c)What is the magnitude of the force an electron, with mass me and charge −e, would feel if placed at this distance from the wire?
I have tried working this over and over and have no idea how to solve it. Any help would be appreciated. Thanks!
Answers & Comments
Verified answer
the electric field will always point directly away from the wire
at any distance r, the electric field will have a magnitude of lambda/(2 pi epsilon 0 r)
this is the result of Gauss' Law for a cylinder
the force of an electric field on a charged particle is F = q E
substitute the values for lambda and r and you should be able to compute all these answers
I'm not sure but doesn't the electric field have a direction based on the SIGN of the charge? In other words, I thought in general the electric field points toward a negative charge and away from a positive charge? If so, then the direction at a distance "r" from a long wire would be *radial* but either toward the wire or away from the wire depending on the SIGN of charge on the wire. Since U don't know the sign of the charge on the wire U can't tell which direction (other than radial) it goes.
In part (b), the electric field strength varies as the inverse of the distance "r". This is unlike the field strength between point charges where the field strength varies as the inverse square of the distance and from an area source (like plates) where the field strength is constant (doesn't vary with distance).
In part (c) the electric force doesn't depend on mass is just: Fe = KQ/r (where Q = -e)