Table of Contents
Magnetic Field of a Wire
A straight current-carrying wire generates a circular magnetic field around it. The field lines form concentric circles centered on the wire, with the direction given by the right-hand rule: if the thumb points in the direction of current flow, the curled fingers indicate the field direction. The field strength is directly proportional to the current and inversely proportional to the distance from the wire.
This relationship, derived from Ampere's law (or equivalently the Biot-Savart law for the infinite wire case), is one of the most fundamental results in electromagnetism. It underlies the operation of electromagnets, transformers, and electric motors, and was first discovered by Oersted in 1820 when he observed a compass needle deflect near a current-carrying wire.
Ampere's Law Formula
Where B is the magnetic field strength (T), μ0 = 4π × 10-7 T·m/A is the permeability of free space, I is the current (A), and r is the perpendicular distance from the wire (m).
Practical Examples
| Scenario | Current | Distance | B Field |
|---|---|---|---|
| Household wire | 15 A | 10 cm | 30 μT |
| Power line | 1000 A | 10 m | 20 μT |
| Lab experiment | 5 A | 1 cm | 100 μT |
| For reference: Earth's field | -- | -- | 25-65 μT |
Frequently Asked Questions
What direction does the field point?
Use the right-hand rule: point your right thumb in the direction of conventional current (positive to negative). Your fingers curl in the direction of the magnetic field. For a wire carrying current upward, the field circles counterclockwise when viewed from above. The field is always tangent to the circular field lines.
Does this formula work for finite-length wires?
This formula assumes an infinitely long straight wire. For finite wires, the field is weaker because the wire subtends a smaller angle. The general formula involves the angles to the wire endpoints: B = μ0 I/(4πr) (sinθ1 + sinθ2). The infinite wire result is recovered when both angles approach 90 degrees.
How does the field from power lines affect health?
Typical magnetic fields from power lines at residential distances (30-100 m) are 0.1-1 μT, well below Earth's field of 25-65 μT. Extensive epidemiological research has not established a causal link between these low-frequency fields and adverse health effects, though research continues on potential mechanisms.