Magnetic Effect of Steady Current

Explore how steady currents generate magnetic fields and how those fields interact with current elements, loops, and straight conductors, including the resulting magnetic forces.

Explore how cgs emu current units relate to si, defining current as charge per second and deriving the abampere and emu equivalents for understanding electromagnetic units.

Explore the Biot–Savart law for steady currents, deriving magnetic induction and magnetic field at a point from a current element, using integration and geometry.

Compute magnetic induction at a point a normal distance x from a finite straight current-carrying conductor using Biot–Savart integration, and show the long-conductor limit B = μ0 I /(2π x).

This lecture derives the axial magnetic induction of a circular current-carrying conductor by integrating its elements, yielding B = μ0 I R^2 / [2(R^2 + x^2)^(3/2)], maximized at the center.

Compute the magnetic induction on the axis of a finite solenoid by integrating over its windings. The result depends on radius and axial distance and remains finite for finite length.

Explore the elementary concept of vector potential and its relation to the magnetic field, showing how current elements produce magnetic induction and how divergence and curl relate to the field.

Explore how a current element produces magnetic induction and compute the divergence of B, showing div B equals zero and supporting the nonexistence of magnetic monopoles.

Examine the derivation of Ampere's law, linking current loops to magnetic induction B, using the curl of B, delta function properties, and the continuity equation to obtain the steady-current form.

Explain how the magnetic vector potential under Coulomb gauge yields Ampere's law via Stokes' theorem, linking the line integral of B to curl A and highlighting zero divergence.

Discover how external electric and magnetic fields produce static and Lorentz forces on charges, including the Lorentz force q v × B for moving charges and current elements.

Explain how a current element experiences a magnetic force from an external magnetic induction, yielding F = I dl × B and discussing uniform versus varying B.

Compute the magnetic force between two long straight current-carrying conductors using Biot-Savart law and superposition, showing mutual forces are equal and opposite per Newton's third law.

Analyze the force between two current carrying conductors by examining elemental current segments. Show that the mutual forces are equal and opposite, upholding Newton's third law.

Explore the concept of magnetic scalar potential in regions with zero current density, highlighting its conservative nature, the nonexistence of magnetic monopoles, and its analogy to a magnetic dipole.

Explore how the magnetic scalar potential of a current loop arises by summing the contributions of many small elementary current elements, integrating (dℓ · R)/R^3.