Find the time dependent magnetic field intensity

[TheBigDig]

Homework Statement

Calculate the time-dependent magnetic field intensity B(t) at an axial distance r from a long, thin straight copper wire that carries a sinusoidal current with an alternating frequency of 50 Hz and a maximum amplitude of 0.5 A.

Homework Equations

$$I = Asin(\omega t)$$
$$B = \frac{\mu_0 I}{2\pi r}$$

The Attempt at a Solution

I can solve for the above simply enough but my real concern is that using this equation for B is greatly oversimplifying the problem. I have looked into using Faraday's Law and Biot-Savart Law but I feel I'm lacking some information in order to use them.

 

[Charles Link]

Homework Statement

Calculate the time-dependent magnetic field intensity B(t) at an axial distance r from a long, thin straight copper wire that carries a sinusoidal current with an alternating frequency of 50 Hz and a maximum amplitude of 0.5 A.

Homework Equations

$$I = Asin(\omega t)$$
$$B = \frac{\mu_0 I}{2\pi r}$$

The Attempt at a Solution

I can solve for the above simply enough but my real concern is that using this equation for B is greatly oversimplifying the problem. I have looked into using Faraday's Law and Biot-Savart Law but I feel I'm lacking some information in order to use them.

What you did is correct. In general, a changing magnetic field can induce an electric field and thereby produce additional results, particularly if there is a conductive medium nearby. In addition, a changing current in a wire can generate electromagnetic waves, but I believe that is more of a concern at r-f frequencies. The magnetic field is a vector though, so you do need to specify the direction. $\\$ Editing: It only asks for the magnetic field intensity, so what you did is sufficient, once you compute the numerical value.

 

[TheBigDig]

Oh thanks very much. That clears things up a lot!