Lenz's Law

What this figure shows. A rectangular metallic frame ABCD sits in a uniform magnetic field directed into the page (shown by crosses), with one arm AB free to slide left or right along the frame's rails. Panel (a) shows AB at rest, with no current flowing. Panel (b) shows AB sliding to the RIGHT, enlarging the enclosed area and hence increasing the flux through the loop; the induced current is shown flowing anticlockwise, and red circular field-line symbols around the loop show that this current creates its own magnetic field pointing OUT of the page inside the loop, opposing the increasing inward flux. Panel (c) shows AB sliding to the LEFT, shrinking the area and decreasing the flux; the induced current now flows clockwise, and the red crosses show its self-field pointing INTO the page, reinforcing (opposing the decrease of) the existing inward flux. The figure is the clearest possible picture of Lenz's law in action: whichever way the flux tries …

What this figure shows. A bar magnet, north pole leading, is moved towards and then away from a coil connected to a galvanometer G, across three panels. Panel (a) shows the magnet at rest and far from the coil, with no deflection. Panel (b) shows the magnet's north pole approaching the coil: the galvanometer deflects, and the near end of the coil is shown becoming a NORTH pole itself (an induced magnetic dipole), so that it REPELS the approaching magnet's north pole -- opposing the magnet's motion towards the coil, exactly as Lenz's law demands. Panel (c) shows the magnet's north pole being withdrawn: the near end of the coil now becomes a SOUTH pole instead, ATTRACTING the receding magnet and again opposing the change (this time opposing the magnet moving away). The figure demonstrates that Lenz's law can be applied either through flux-based reasoning or, equivalen …

Worked out. A straight current-carrying wire runs near a metallic square loop, and the current i in the wire is decreasing; the direction of the induced current in the loop is required. By the right-hand rule, the straight wire's own magnetic field passes through the loop directed INTO the plane of the loop, and because i is decreasing, this inward flux through the loop is decreasing. By Lenz's law, the induced current must oppose this decrease, so it flows in whatever sense creates a magnetic field of its own that reinforces (adds to) the existing inward field inside the loop. Applying the right-hand rule again to find which current direction produces an inward self-field, the induced current in the loop is found to flow CLOCKWISE (as viewed from the same side as the straight wire), showing how Lenz's law and the right-hand rule co …

Worked out. The flux through a circuit, directed into the page, varies as $\Phi_B(t) = (2t^3+3t^2+8t+5)$ mWb, and the emf and current direction at t = 3 s are required. Differentiating, $\varepsilon = -N\dfrac{d\Phi_B}{dt} = -(6t^2+6t+8)\times10^{-3}$ V; at t = 3 s this gives $\varepsilon = -(6(9)+6(3)+8)\times10^{-3} = -(54+18+8)\times10^{-3} = -80\times10^{-3}$ V, so the induced emf has magnitude 80 mV. Since every term in $\dfrac{d\Phi_B}{dt}$ is positive for t = 3 s, the flux (which points into the page) is INCREASING with time. By Lenz's law, the induced current opposes this increase by creating a magnetic field pointing OUT of the page inside the loop, which by the right-hand rule means the induced current flows ANTICLOCKWISE. The example combines calculus (differentiating a polynomial flux expression) with the qu …