Lenz' law

CC Image
Illustration of Lenz law. The time derivative $\scriptstyle {\dot {\mathbf {B} }}$ describes an increase of B (vectors parallel) or a decrease of B (vectors antiparallel). In the first case the field due toi_ind weakens B and in the second case it reinforces B.

In electromagnetism Lenz' law states that a change in magnetic flux Φ (magnetic induction B integrated over a surface S, see this article) gives an induced current that opposes the change in flux.

For the sake of argument we consider the case of a time-dependent magnetic induction B(t) passing through a time-independent surface S. Further we assume that B(t) does not vary over the surface. According to Faraday's law of magnetic induction the time derivative of B(t)

${\dot {\mathbf {B} }}\equiv {\frac {d\mathbf {B(t)} }{dt}}$

induces a current i_ind in a conducting loop. The direction of i_ind is such that the change in field B(t) is opposed. The different cases are illustrated in the figure on the right. Recall here that the direction of current i and field B are connected through the right-hand screw rule, that is, a screw is driven in the direction of B and rotated in the direction of i.

The law is named for the Estonian physicist Emil Lenz (1804 – 1865), who published his law in 1834, shortly after Michael Faraday's 1831 discovery of currents induced by moving magnets. Lenz enunciated his law as follows: when a conducting circuit is moved in a magnetic field, the induced current flows in such a direction that the force on it tends to oppose the motion.