# Magnetic Field and Current Relationship

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?

• Please add an image. I am not able to interpret your ASCII image. – Yashas Feb 24 '17 at 5:42

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 :

1. Increasing the distance between the current carrying wire and point P
2. Decreasing the current

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.

• okay that makes sense now if the direction of the magnetic field at P is reversed could that be due to the reversing of the current or moving point P below the wire at the same distance? – Dee Feb 24 '17 at 6:24
• Both. Assume that there is a current carrying wire, with the current going into the screen through it's centre and there is point P at the left of your screen, then the magnetic field on point P will be upwards. If now you, put the point P below the wire or at the lowest point on your computer screen, the direction of magnetic field will be towards the left. Reversing the current will change the direction of magnetic field from upwards to downwards and left to right in the above cases respectively. Are you familiar with the right hand thumb rule. If not, then you should check it out. – Mitchell Feb 24 '17 at 6:33

The magnetic field at a point due to a long wire is

$$B = \frac{\mu i}{2\pi d}$$

So the field is inversely proportional to the distance from the wire.

So the field decreases due to the distance increases that is $P$ moves further away or current decrease.

If the direction of the magnetic field is reversed, then either direction of current is reversed or point is on the other side of wire