Q.A flexible metallic loop abcd in the shape of a square is kept in a magnetic field with its plane perpendicular to the field. The magnetic field is directed into the paper normally. Find the direction of the induced current when the square loop is crushed into an irregular shape as shown in the figure.

Statement. Lenz's law, formulated by the German physicist Heinrich Lenz, gives the DIRECTION of an induced current (which Faraday's laws alone do not specify): the direction of the induced current is always such that it opposes the cause responsible for its production. If a changing flux is the cause and an induced current the effect, the induced current always acts, through the magnetic field it itself creates, to oppose that very flux change.

In the emf formula. Incorporating Lenz's law into Faraday's law supplies the standard minus sign, $\varepsilon=-d(N\Phi_B)/dt$ -- not a mathematical formality, but a literal encoding of the physical statement that the induced emf's polarity always opposes the flux change producing it.

Application technique. To find a direction: (i) determine whether the relevant flux is increasing or decreasing; (ii) the induced current flows in whichever sense creates its OWN magnetic field that opposes that particular change (reinforcing a decreasing flux, or counteracting an increasing one); (iii) apply the right-hand rule to that self-field to read off the current's actual direction around the loop. Equivalently, for a magnet approaching/receding a coil, the coil's near end becomes whichever pole (N or S) repels an approaching magnet or attracts a receding one. …