Magnetic Fields due to Electric Current

Magnetic force is always perpendicular to velocity, Magnetic force does no work on moving charges, Magnetic force depends on the charge and velocity

From F⃗ = q(v⃗ × B⃗): (1) Force is perpendicular to both v⃗ and B⃗, (2) Since F⃗ ⊥ v⃗, work = F⃗·v⃗ = 0, (3) Force can only change direction, not speed, (4) Force depends on q, v, and B, (5) Force is zero when v⃗ ∥ B⃗

Tesla (T)

The SI unit of magnetic field is Tesla (T). 1 T = 1 N·s/(C·m) = 1 Wb/m². Gauss is a non-SI unit where 1 T = 10⁴ G. Weber is the unit of magnetic flux, and Henry is the unit of inductance.

Electric motor, Moving coil galvanometer, Loudspeaker

Electric motors use magnetic force on current-carrying coils to produce rotation. Moving coil galvanometers measure current using deflection of coil in magnetic field. Loudspeakers use magnetic force on voice coil to produce sound. Transformers use electromagnetic induction, electromagnets create magnetic fields.

3.77 × 10⁻³ T

For solenoid: B = μ₀ni, where n = turns per unit length, i = current. Given: n = 1000 turns/m, i = 3 A. B = 4π × 10⁻⁷ × 1000 × 3 = 12π × 10⁻⁴ = 3.77 × 10⁻³ T