A charge of 7.4 `microC is uniformly distributed on a wire 35 meters long. Use the flux model to determine the electric field at a distance of .1 meters from the wire, at a point far from the ends of the wire. Repeat for a point at .16 meters, again far from the ends of the wire.
We calculate the flux over cylinders which surround the wire at uniform distances of .1 meters and .16 meters.
The total flux is 4`pi kq, where q is the total charge 7.4 `microC. This flux is 4`pi (9 x 10^9 N m^2/C^2 ( 7.4 `microC)) = 836900 N m^2/C.
The total surface area of the cylinder is 35 meters (2`pi ( .1 m))) = 21.99 m^2.
The magnitude of the electric field is flux / area = ( 836900 N m^2 / C) / ( 21.99 m^2 ) ) = 38050 N / C.
At a distance of .16 meters from the wire, the flux would be evenly spread over a cylinder 35 m long and with radius .16 meters.
- electric field = flux / area = ( 836900 N m^2 / C) / ( 35.18 m^2) = 23780 N / C.
A total charge Q will produce flux 4 `pi k Q.
If the charge is evenly distributed on a wire of length L, then a cylinder of radius r and length L will have total area 2 `pi r L on its curved surface.
If the cylinder is uniformly penetrated by all the flux produced by the charge, the flux density on this curved surface will be the electric field strength:
This can be written as
where the Greek letter `lambda is the charge / unit length along the wire.
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