Electric Field of Line Charge

The electric field of an infinite line charge with a uniform linear charge density can be obtained by a using Gauss' law. Considering a Gaussian surface in the form of a cylinder at radius r, the electric field has the same magnitude at every point of the cylinder and is directed outward. The electric flux is then just the electric field times the area of the cylinder.

Field for finite line charge
Charged conducting cylinderCylinder of uniform charge
Fields for other charge geometries
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Electric field concepts
 
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Electric Field: Conducting Cylinder

The electric field of an infinite cylindrical conductor with a uniform linear charge density can be obtained by using Gauss' law. Considering a Gaussian surface in the form of a cylinder at radius r > R, the electric field has the same magnitude at every point of the cylinder and is directed outward. The electric flux is then just the electric field times the area of the cylinder.

Line chargeCylinder of uniform charge
Fields for other charge geometries
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Electric field concepts
 
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Electric Field:Cylinder of Charge

The electric field of an infinite cylinder of uniform volume charge density can be obtained by a using Gauss' law. Considering a Gaussian surface in the form of a cylinder at radius r > R, the electric field has the same magnitude at every point of the cylinder and is directed outward. The electric flux is then just the electric field times the area of the cylinder.

Show form inside cylinder
Line chargeCharged conducting cylinder
Fields for other charge geometries
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Electric field concepts
 
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Inside a Cylinder of Charge

The electric field inside an infinite cylinder of uniform charge is radially outward (by symmetry), but a cylindridal Gaussian surface would enclose less than the total charge Q. The charge inside a radius r is given by the ratio of the volumes:

The electric flux is then given by
and the electric field is
Note that the limit at r= R agrees with the expression for r >= R.
Field outside charged cylinder
Index

Electric field concepts
 
HyperPhysics***** Electricity and Magnetism R Nave
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