Fix the mistake: Electromagnetism and Circuits

Electric Current, Magnetic Field, and Ampère’s Law

Electric current produces a magnetic field, and a magnetic field exerts force on electric current. We will study the core of the interaction in electromagnetism.

Basic Knowledge

Magnetic field produced by a straight current (Ampère’s law):
At a point a distance r from current I: B = μ₀I/(2πr)
Direction: right-hand screw rule (when a right-handed screw advances in the direction of the current, the direction of rotation is the direction of the magnetic field)

Magnetic field at the center of a circular current:
B = μ₀I/(2r) (r: radius of the circle)

Magnetic field inside a solenoid:
B = μ₀nI (n: number of turns per unit length)

Permeability of free space: μ₀ = 4π × 10⁻⁷ T·m/A

Force acting on a current in a magnetic field (Ampère force):
F = BIL sinθ (L: length of the current, θ: angle between the magnetic field and current)

Further Study (Background and Significance)

The attraction and repulsion of two parallel currents is an application of the Ampère force: currents in the same direction attract, while currents in opposite directions repel. The unit of current, the “ampere,” was formerly defined using this force (before the 2019 revision).
The magnetic field of a solenoid, B = μ₀nI, does not depend on the length or cross-sectional area of the coil. MRI (magnetic resonance imaging) systems use superconducting coils to create powerful uniform magnetic fields (several teslas).
The tesla (T), the basic unit of magnetic field, represents a very strong field: Earth’s magnetic field is approximately 5 × 10⁻⁵ T, MRI systems are 1.5 to 3 T, and experimental superconducting magnets can achieve more than 20 T.

Points to Note (Easily Confused)

① Always determine the magnetic-field direction using the right-hand screw rule (do not confuse it with the left-hand screw rule). ② Determine the direction of the Ampère force using Fleming’s left-hand rule (middle finger: current, index finger: magnetic field, thumb: force). ③ F = BIL applies when θ = 90°. In general, do not forget sinθ. ④ “Magnetic field H” and “magnetic flux density B” are different quantities. In high-school physics, B is used.

Practice

1. Find the magnetic flux density at a point 0.10 m from a straight current of 5.0 A (μ₀ = 4π × 10⁻⁷ T·m/A).
2. Find the magnetic flux density inside a solenoid (n = 1000 turns/m, I = 2.0 A).
3. Find the force on a 0.20 m current carrying 3.0 A, placed perpendicular to a magnetic field with flux density 0.50 T.