Why gradient must exist to make electric field in a wire or pipe?
Answers
The electric field E in a conductor is a consequence of the resistive action of the conductor to the passage of electric current. It is much like the formation of a pressure gradient due the passage of fluid in a tube. The free electrons in a conductor drift under the influence of electric field.
This matter of fact is expressed mathematically in the form:
E= J/ sigma,
where J is the current density and sigma is conductivity of the conductor.
Expressed in an other way, Because of the electric field associated with the passage of
current in a conductor, a voltage is measured across it. This voltage V is the integration of E along the path of the current in the conductor. If the conductor is homogeneous with length L, then V= EL.
The opposite is true. That is if a voltage V is applied on the conductor, an electric field E will be formed in it and and a current with a density J will flow along the conductor.
Practically, one can use a dc electric source with a driving electromotive force of V to pass a current density J in the conductor. The dc source may be a battery or a dc power supply.
The interior of the conductor remains neutral during the passage of the drift current in it.
Charge accumulation and de accumulation occurs during charging and discharging of the capacitors. The electric field formed in the insulator of the capacitor is associated with stored charges on the capacitor metallic plates.
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