# Any deep cause of magnetic field

#### Nikaro

when we apply potential difference across any conductor the electric field set up in the conductor which apply force on charged particals and set up moving current.While the current is moving the charge which is at the outer surface of conductor also make elecricfield which is moving along the conductor.
Is this moving electric field is the cause of magnetic field ?
If it is not than please please tell me the reason of magnetic field?
And is there is any deep relation between magnetic and electric field.

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#### Cyosis

Homework Helper
Not sure what you mean by a moving electrical field. Moving charges produce a magnetic field, but also an electrical field that changes with time produces a magnetic field.

I think one of the nicest and deepest understanding of magnetic fields arise from special relativity. Where a magnetic and electric field are part of the same phenomenon. Different observers will see different type of fields.

#### Bob S

One reason is that curl H = J, meaning that currents are the cause of magnetic fields. Another reason (which you point out) is that a Lorentz transformation on an electric field creates a magnetic field. A time-dependent magnetic field does create electric fields (curl E = - dB/dt), but a time dependent electric field (=dE/dt) cannot create a magnetic field.

#### Cyosis

Homework Helper
Bob S said:
A time-dependent magnetic field does create electric fields (curl E = - dB/dt), but a time dependent electric field (=dE/dt) cannot create a magnetic field.
Could you elaborate on this seeing as

$$\nabla \times \vec{B}=\mu_0 \vec{J}+\mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}$$.

#### Bob S

Could you elaborate on this seeing as

$$\nabla \times \vec{B}=\mu_0 \vec{J}+\mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}$$.
Mea culpa. I should have included the displacement current term, which makes the Curl E and Curl H equations more symmetric, and is very important in electromagnetic radiation, especially when there are no conductors around.

#### cabraham

E & H are mutually inclusive under dynamic conditions, i.e. one cannot exist w/o the other. If one is time-changing, the other must be non-zero. Einstein in his 1905 paper, described that neither one is the "seat" ("seat" meaning basis or primary).

Claude

#### Bob S

There is another source of a magnetic field. A transverse electric field in one reference frame can be converted into a transverse magnetic field in another reference frame by a Lorentz transformation:

BT' = γBT - (γ/c2) v x ET

α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ ς σ τ υ φ χ ψ ω . . . . . Γ Δ Θ Λ Ξ Π Σ Φ Ψ Ω

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