Ch 12Electromagnetic Induction — Class 12 Physics, concept-first.

By the early nineteenth century, Oersted, Ampere and others had shown that an electric current produces a magnetic field around it.

Faraday distilled his experimental observations into two laws. The First Law (a qualitative law) states that whenever the magnetic flux linked with a closed circuit changes, an emf is induced in it; e…

Faraday's second law gives the magnitude of the induced emf but says nothing about its direction. That gap was filled by H.F.E.

Consider the north pole of a bar magnet approaching a stationary conducting loop. As the magnet nears the loop, the flux linked with the loop (in the direction leading away from the magnet's north pol…

Lenz's law is not an independent postulate -- it is forced on us by the law of conservation of energy.

The minus sign in is not a mere convention -- it is Faraday's law's built-in encoding of Lenz's law. To see this, fix the loop's area vector (perpendicular to the loop's plane) so that it points paral…

The concept of magnetic flux is central to Faraday's law. Consider a small element of area : by convention, a direction is assigned to this area element such that if the boundary curve is traversed in…

An emf induced specifically because a CONDUCTOR is physically moving through a magnetic field (rather than because the field itself is changing at a fixed location) is called a motional emf.

Consider a C-shaped conducting frame ABCD of wires, with a straight conducting rod BC of length l free to slide along the frame (parallel to AD) in a uniform magnetic field perpendicular to the plane…

A rotating bar is a genuinely different case from a sliding bar, because different points along its length move at different speeds.

This section studies the complementary case to motional emf: a coil that is itself completely stationary, sitting in a magnetic field whose STRENGTH varies with time.

An electric generator's basic construction mirrors that of the electric motor studied earlier: an armature (a coil) is mounted so it can rotate within a magnetic field, but where a motor is driven ele…

Faraday's principle applies to every source of emf, not only coils in changing fields: chemical action produces emf in a battery, mechanical pressure in a piezoelectric crystal, a temperature gradient…

Consider a rectangular conducting loop ABCD being pulled with constant velocity out of a region of uniform magnetic field (the dashed lines in the standard figure mark the field's boundary).

If the conducting LOOP of the previous section is replaced by a solid conducting PLATE, the same relative motion between conductor and field still induces a current -- but now, instead of being confin…

Consider an isolated circuit (coil) carrying a current that is CHANGING with time. The changing current itself continuously alters the magnetic flux that this same current sets up and links through it…

Building up a steady current in an inductor requires doing work AGAINST the self-induced back-emf, and this work does not vanish -- it is stored as energy in the magnetic field the current establishes…

This section derives the general energy-density result explicitly for the case of a long solenoid, where the field is confined (to a good approximation) entirely to the solenoid's interior and is unif…

Now consider two separate coils placed near each other, coil 1 and coil 2. A steady current flowing in coil 1 sets up a magnetic field throughout the surrounding region, including at coil 2; the resul…

Mutual inductance is the operating principle behind every kind of transformer -- a device that changes an alternating voltage from one value to another (step-up or step-down), commonly seen mounted on…

Sample papers and previous-year board questions for this subject.