Ampère's Law

Ampère's law says that if you add up the component of the magnetic field tangent to any closed loop, that total circulation is proportional to the current passing through the loop. Physically, this expresses the fact that electric current is a source of curling magnetic fields, which is why fields wrap around wires and coils instead of pointing straight out like electric fields do. In highly symmetric situations, it lets you turn a difficult field calculation into a simple current-counting problem.

Use this law when the current distribution has enough symmetry to make the magnetic field easy to relate to a closed path, such as around a long straight wire, inside a solenoid, or around a toroid. It is especially useful in electromagnetism problems where you need the magnitude of vec{B} from a known current.

• Forgetting that the line integral is around a closed loop, not a straight line
• Using the law without symmetry, when the field is not constant along the chosen path
• Mixing up current direction and magnetic-field direction; use the right-hand rule to get the sign and orientation