A current-carrying wire produces a magnetic field, concentric about the wire.
Magnetic field of a current-carrying wire
We can use the Biot-Savart law to derive the magnetic field of multiple charges moving, such as in a current-carrying wire.
Replacing q Δv with I Δs gives us the equation for a short segment of a current carrying wire.
To find the formula for the magnetic field at a point P, a distance d away from a long current-carrying wire, we need to integrate over current segments.
We define the useful quantities sin θ and r for our system at hand and substitute into the segment equation.
Integrating over all of the segments, we approximate a long wire by setting our limits for an infinitely long wire.
Evaluating at these limits gives us a relatively simple equation for the magnetic field of a current-carrying wire.
The diagram above shows the B field of a current-carrying wire.
The direction of the positive current is into the page, marked by an "x."
The magnetic field of the wire is in the shape of concentric circles about the wire.
Notice the circles get farther apart as the distance from the wire increases,
indicating that the strength of the B field decreases with distance.
This diagram shows the current-carrying wire at an angle. Here, the direction of the B field at particular
points about the wire is shown as arrows. Not that the arrows are longer in the inner circles, closer to the wire.
The right-hand rule for a current-carrying wire is illustrated above.
The hand grasps the wire with the thumb in the direction of the current.
The fingers wrap around the wire, giving the direction of the B field in the concentric circles.
Sample questions
1. What is the direction of the magnetic field at point P, due to this current-carrying wire?
A. up
B. down
C. right
D. left
E. into the page
F. out of the page
2. Where is the magnetic field stronger, at A or B??
