time varying electric field

in many books they given that, the time varying electric field created when charges are moving.if the dc current moving a conductor in constant rate means the electric field in the conductor is constant or varied.if it is constant means how the magnetic field created by the dc current.

The constant electric field can produce the magnetic field. Ther is no need of varying electric field. The varying electric field is only neccessary for the mutual inducation. So the constant DC current produce constant magnetic field at constant electric field.

if the constant electric field produce magnetic field means how it satisfies the Maxwell's equation.

low frequency limit electric fields and magnetic fields are decoupled.

i couldn't understood,please explain.

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i have two doubts,1. what is the difference between magnetic field produced by constant and time varying electric field.
2.what difference make when current flow through normal wire and wounded wire around any core(inductor).

rameshbalan said:

if the constant electric field produce magnetic field means how it satisfies the Maxwell's equation.

Click to expand...

I think that you are mixing a few different ideas resulting in the confusion.

1. To setup a DC current, a constant E-field is applied across the conductor - which results in motion of the charges.

2. The charges moving within the conductor will create an electric/magnetic field. This is what is commonly referred to as magnetic field generated by a current carrying wire. (see https://en.wikipedia.org/wiki/Ampère's_circuital_law ).

Note: The changing E-field resulting in H-field refers to the point in space where you see the H-field (and not a changing E-field in the source location).

The difference between the current flowing into the straight normal wire and wounded wire like an inductor is the magnetic field generated by the normal straight wire is constant throughout the wire whereas in case inductor the wire is now beheaving like a loop and now the magnectic field genrated is not constant throughout the inductor. It become the distance dependent. So the magnetic field inside (Center) of inductor is max and decreasing outward along the central axis. And if u plot the graph between the magnetic field and distance inside the inductor............. It is platau type.......

rameshbalan said:

i couldn't understood,please explain.

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i have two doubts,1. what is the difference between magnetic field produced by constant and time varying electric field.
2.what difference make when current flow through normal wire and wounded wire around any core(inductor).

Click to expand...

1. Constant electric field cannot produce magnetic field. It is only the moving charges which produce changing electric field which produces magnetic field.

2. Comparing a wire carrying a current I to a wound coil (solenoid) carrying current I,

Field produced by wire: \[ B = \frac{\mu_0 I}{ 2 {\pi} r} \]
(drops as a function of 1/r with distance away from wire)

Field produced within the solenoid: \[ B = \mu_0 N I \]
(almost constant within the central region of the solenoid)

Constant means not changing over time. Start from fundamental laws (Column's law). If there is a static charge sitting in space, only electric field exists. And it can be calculated through Gaussian's law. Divergence of the field is equal to the total charge within the closed surface. No magnetic field in such case.

When charge moves, It becomes time varying, since motion need speed, which is distance over time. Thus it creates time varying electric field. Then according to Faraday and Ampere's law, time varying E field creates space varying H field, and vise versa. This makes the E and H field co-exists and sometimes propagate.

Maxwell's equations summarize Faraday, Ampere, Gaussian's law together, it contains 4 equations and is complete in describing E and H fields in non-relativity scope.