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edit: Trying to find the magnetic field generated by a time dependent oscillating current.

The current is flowing through a long, thing wire that is laying on the z-axis. The perpendicular distance from the z-axis is given a. If $z=0$, we can write the current as

$$ I(t)=I_0\sin \omega t $$ and now I am trying to find the magnetic field at $z=0$ with this current. How can we calculate $\vec B$?

Possibly, can we calculate $\vec J$ to calculate $\vec A$ to calculate the magnetic field?

THanks a lot for your help on the last problem too.

edit: Hi I'm trying to find the magnetic field generated by a time dependent oscillating current in the quasistatic case ($|z|,r <<c\omega$) where r is the perpendicular distance from the z-axis.

The current is flowing through a long, thing wire that is laying on the z-axis. If $z=0$, we can write the current as

$$ I(t)=I_0\sin \omega t $$ and now I am trying to find the magnetic field $B(r,t)$ at $z=0$ with this current. How can we calculate $\vec B$?

Possibly, can we calculate $\vec J$ to calculate $\vec A$ to calculate the magnetic field?

THanks a lot for your help on the last problem too.

Is there an easy/general way to calculate $\vec J$ from the current I, if the current is Time Dependent? $\vec J$ is the current density.

The current is flowing through a long, thing wire that is laying on the z-axis. The perpendicular distance from the z-axis is given a. If $z=0$, we can write the current as

$$ I(t)=I_0\sin \omega t $$ and now I am trying to find the magnetic field at $z=0$ with this current. How can we calculate $\vec B$?

Possibly calculate $\vec J$ to calculate $\vec A$ to calculate the magnetic field.

THanks a lot for your help on the last problem too.

edit: Trying to find the magnetic field generated by a time dependent oscillating current.

The current is flowing through a long, thing wire that is laying on the z-axis. The perpendicular distance from the z-axis is given a. If $z=0$, we can write the current as

$$ I(t)=I_0\sin \omega t $$ and now I am trying to find the magnetic field at $z=0$ with this current. How can we calculate $\vec B$?

Possibly, can we calculate $\vec J$ to calculate $\vec A$ to calculate the magnetic field?

THanks a lot for your help on the last problem too.

Is there an easy/general way to calculate $\vec J$ from the current I, if the current is Time Dependent? $\vec J$ is the current density.

I am just looking for a general method (I will apply it to my problem).

THanks a lot for your help on the last problem too.

Is there an easy/general way to calculate $\vec J$ from the current I, if the current is Time Dependent? $\vec J$ is the current density.

The current is flowing through a long, thing wire that is laying on the z-axis. The perpendicular distance from the z-axis is given a. If $z=0$, we can write the current as

$$ I(t)=I_0\sin \omega t $$ and now I am trying to find the magnetic field at $z=0$ with this current. How can we calculate $\vec B$?

Possibly calculate $\vec J$ to calculate $\vec A$ to calculate the magnetic field.

THanks a lot for your help on the last problem too.