The magnetic field set up at point P by the current element i ds
The above equation is called the Biot-Savart law.
However, the current must form a loop. You will not have only a small current element.
All the current elements along the current loop can contribute to the magnetic field at point P.
How do we measure magnetic field dB just due to a small current element?
Here is an ideal!
There is no magnetic field in the direction of the current element.
The above two green lines meet at blue dot P.
Current elements from green lines will not produce magnetic field at point P.
The magnetic field at point P is due to current elements from two yellow line sections.
We can keep one of the current element much further away from point P.
Now we have a way to measure the magnetic field just due to one current element.
Click near the left yellow line section and drag the mouse up/down or left/right
The magnetic field at point P is shown at the top left corner.
Click at the DC current source to change its polarity.
You can enter value for the current source into the text Field.
The moving black points represent the electrons moving with average drift velocity.
If you enter a larger value for the current , the electrons will move faster.
Keep increasing the value for the current, until you see the electrons
Look at tires of a car when it is accelerating!
Those tires seem to be rotated faster and then change direction ... !