Magnetic field of a straight current-carrying conductor

[PhysicsTest]

Homework Statement

To find the magnetic field in a straight current carrying conductor due to sine wave at a distance x on its perpendicular bisector.

Relevant Equations

$B = \frac {\mu_0 I 2a} {4\pi x\sqrt{x^2 + a^2}}$

It is not a direct home work problem, i was thinking if a sine wave current passes through the straight current carrying conductor, what will be the magnetic field. For the DC current I know the formula as below.
$B = \frac {\mu_0 I 2a} {4\pi x\sqrt{x^2 + a^2}}$
Let the current be $I = I_0\sin(\omega t)$ then will the magnetic field be
$B = \frac {\mu_0 I_0\sin(\omega t) 2a} {4\pi x\sqrt{x^2 + a^2}}$

 

[berkeman]

Homework Statement:: To find the magnetic field in a straight current carrying conductor due to sine wave at a distance x on its perpendicular bisector.
Relevant Equations:: $B = \frac {\mu_0 I 2a} {4\pi x\sqrt{x^2 + a^2}}$

It is not a direct home work problem, i was thinking if a sine wave current passes through the straight current carrying conductor, what will be the magnetic field. For the DC current I know the formula as below.
$B = \frac {\mu_0 I 2a} {4\pi x\sqrt{x^2 + a^2}}$
Let the current be $I = I_0\sin(\omega t)$ then will the magnetic field be
$B = \frac {\mu_0 I_0\sin(\omega t) 2a} {4\pi x\sqrt{x^2 + a^2}}$

Could you attach a diagram showing what $x$ and $a$ are in your question?

And yes, if the wavelength of the B-field sinusoid (propagating at c) is long compared to how close to the wire you want your solution to work, then you just multiply by the sinusoid function itself. If that condition does not hold, then there will be a phase shift between the driven current in the wire and the B-field sensed away from the wire. Does that make sense?

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html

 

[PhysicsTest]

The diagram is

If that condition does not hold, then there will be a phase shift between the driven current in the wire and the B-field sensed away from the wire.

How do I calculate the phase shift? Can you provide a hint, I will attempt.

 

[BvU]

It is not very realistic to let the current vary with such a high frequency that the propagation to point P is influenced, without considering what happens to the charge in the conductor.

Perhaps you want to look at the phenomena associated with a radiating dipole ?