Ampere's law connects electric current to the magnetic field that curls around it. It is one of Maxwell's equations and is essential for understanding electromagnets, motors, transformers, and magnetic sensors. A long straight wire produces circular magnetic field lines, while a solenoid concentrates those field lines into a strong, nearly uniform field inside the coil.
This law matters because it lets you calculate magnetic fields from the currents that create them.
Key Facts
- Ampere's law: ∮B · dl = μ0 Ienc
- Magnetic field around a long straight wire: B = μ0 I / (2πr)
- Magnetic field inside a long solenoid: B = μ0 n I
- Permeability of free space: μ0 = 4π × 10^-7 T·m/A
- Right-hand rule for a wire: thumb points with current, curled fingers show magnetic field direction.
- For a solenoid, n = N / L, where N is the number of turns and L is the solenoid length.
Vocabulary
- Ampere's law
- A law stating that the circulation of the magnetic field around a closed path equals μ0 times the current enclosed by that path.
- Amperian loop
- An imaginary closed path used to apply Ampere's law to a symmetric magnetic field.
- Magnetic field
- A vector field that describes the magnetic force influence around currents, magnets, and changing electric fields.
- Solenoid
- A coil of wire that produces a strong magnetic field inside when electric current flows through it.
- Right-hand rule
- A direction rule that relates the direction of current to the direction of the magnetic field it creates.
Common Mistakes to Avoid
- Using total current instead of enclosed current is wrong because Ampere's law only counts current passing through the surface bounded by the chosen loop.
- Forgetting that B is a vector is wrong because the dot product B · dl depends on whether the field points along the loop direction.
- Using B = μ0 I / (2πr) for any wire is wrong because that formula assumes a long straight wire with cylindrical symmetry.
- Applying B = μ0 n I near the ends of a short solenoid is wrong because the simple formula works best for a long solenoid where the interior field is nearly uniform.
Practice Questions
- 1 A long straight wire carries a current of 8.0 A. Calculate the magnetic field strength 0.040 m from the wire.
- 2 A solenoid has 600 turns and is 0.30 m long. If it carries a current of 2.5 A, calculate the approximate magnetic field inside the solenoid.
- 3 A circular Amperian loop is drawn around two wires, one carrying 5 A out of the page and one carrying 3 A into the page. Explain how to determine the net enclosed current and the direction of the magnetic field circulation.