I have a point that is located right above a long straight wire with a current towards the right.
Now, my question is the following:
If the magnetic field at P decreases, but the direction remains the same, was this caused by an increase in the current, a reversing on the direction of the current, moving P farther away from the wire, moving P closer, moving P below the wire with the same distance, or any other reason?
I think that it would be due to the fact that P is moving further away, but I need an explanation and how can we know the strength of the magnetic field?
Best Answer
The magnetic field due to a current carrying wire is given by :
$\vec{dB} = \frac{\mu_\circ}{4\pi}\int \frac{I\vec{dl}\space\times\space\hat{{r}}}{r^2}$
$\vec{r}$ is the point where we want to find magnetic field due to the small current carrying element $\vec{dl}$.
In order to get the magnitude of the magnetic field at a point P, $a$ units away from the wire, we will have to integrate the above equation and, thus adding the magnetic field by all the small $dl$ elements in the current carrying wire of length L.
I'll skip the integration part, and on integrating we get to following formula,
$|\vec{B}|=\frac{\mu_\circ I}{4\pi a} [\sin{\phi_1}+\sin{\phi_2}]$
Therefore, the following factors will decrease the magnetic field at point P :
To determine the direction of the magnetic field you can use the right hand thumb rule:
Imagine holding the current carrying wire in your hand with your thumb pointing in the direction of the current. Now curl you finger around the wire. The fingers will encircle the wire in direction of the lines of magnetic force.