Does B=0 at points out of the plane containing and normal to a point current I?

[Trollfaz]

Consider a point current I flowing at origin in the positive z direction. Biot Savart Law states that B field must move in an anticlockwise circle everywhere with the infinite line that the direction vector of the current, in this case the z axis, at the center. And its strength must be equal at all points as long as $\triangle r$ is equal.
Now using Ampere's law
$$\int_{C}B.dl=\frac{I_{enc}}{\mu_0}$$
Means for a circle of radius r,
$2πrB=\frac{I}{\mu_0}$ in xy plane
$2πrB=0$ else as no current enclosed by circle.
So does this mean there's no magnetic field outside xy plane

 

[Orodruin]

What do you mean by ”point current”? A current existing only at one point? There is no such thing as it would violate conservation of charge implied by Maxwell’s equations.

 

[Trollfaz]

Then for a semi infinite wire starting from z=0 carrying current I in the positive z direction. By Ampere's law, B is 0 if z<0 as a circle encloses no current but clearly it's not.

 

[Orodruin]

A semi infinite wire also violates current conservation. You need to stop making up unphysical scenarios. They all suffer from the same basic flaw.

 

[Baluncore]

Then for a semi infinite wire starting from z=0 carrying current I in the positive z direction. By Ampere's law, B is 0 if z<0 as a circle encloses no current but clearly it's not.

There are many circles you can draw centred on the origin.

Imagine the current at the origin was in a very short dipole.
You can expect a dipole far-field radiation pattern, which is only zero in the directions of ±z .

 

[Orodruin]

Imagine the current at the origin was in a very short dipole.
You can expect a dipole far-field radiation pattern, which is only zero in the directions of ±z

This is not what the OP has in mind. They are imagining a static one-directional current in the origin only, which is unphysical.

In the case of a dipole there is no loop containing any current outside the dipole so all circulation integrals of the magnetic field are zero. For the OP it should be noted that this does not mean that the field is zero. The circulation integral equalling zero is not in itself a sufficient condition to conclude that the field is zero along the closed curve.

 

[Baluncore]

This is not what the OP has in mind.

Do you claim to be a better mind reader than me?

The B field at any point in 3D is the sum of the B field generated by every dz of an infinite wire along the z axis. I am considering only the element dz at the origin.

 

[Orodruin]

Do you claim to be a better mind reader than me?

If you read OP’s other threads you would see where they are coming from and the type of questions being asked at the moment.

I am considering only the element dz at the origin.

This is not what OP is talking about. They are talking about applying Ampere’s law to find the total magnetic field with a current at the origin only:

Now using Ampere's law
∫CB.dl=Iencμ0
Means for a circle of radius r,
2πrB=Iμ0 in xy plane
2πrB=0 else as no current enclosed by circle.
So does this mean there's no magnetic field outside xy plane

 

[vanhees71]

I guess you mean a current along an infinitely thin wire. Then the correct form of

Do you claim to be a better mind reader than me?

The B field at any point in 3D is the sum of the B field generated by every dz of an infinite wire along the z axis. I am considering only the element dz at the origin.

This is utterly misleading, because using the Biot-Savart law only for a finite (or infinitesimal) piece of wire cannot lead to a solution of the (magnetostatic) Maxwell equations, because these can only be solved is $\vec{\nabla} \cdot \vec{j}=0$ everywhere. So for a filamental current you have to integrate along a closed loop or in the (somewhat artificial) limit along an infinite wire and close the loop at infinity.