Result

Induced electric field

(E9.4.1) E9.4 · Induced Electric Fields →

\oint E \cdot d ℓ = - \frac{d Φ _{B}}{d t}

Statement

Faraday's law restated as a statement about the electric field itself, independent of whether an actual wire is present.

Symbols and units

$E$	induced electric field	V/m
$Φ_{B}$	magnetic flux through the loop	Wb
$d ℓ$	line element along the path	m

When it applies

Any region with a changing magnetic flux, whether or not a physical conductor is present.

Don't use when

Describes the field from a changing magnetic flux specifically — a static magnetic field, however strong, induces no electric field at all.

Derivation

The emf around any closed path, wire or not, is by definition the line integral of E around it — restating Faraday's law in these terms gives a field equation rather than a circuit relation.

\oint E \cdot d ℓ = - \frac{d Φ _{B}}{d t}

Watch out for

Unlike an electrostatic field, an induced electric field has closed loop field lines and is NOT conservative — the line integral around a closed path is generally nonzero, so no potential function exists for it.

Connects to

Junction and loop rules