^Eddy currents
Opposing currents produced in the whole volume of a metallic body in the form of closed loops due to the change in magnetic flux linked with a body oppose the change in magnetic flux & can be so strong that the metallic body become red hot.
^Combination of inductors
^Coefficient of coupling (K)
It is defined as, 
(A) The value of K is 0 < K < 1 for loose coupling (i.e. When the axis of two coils are parallel to each other & on different lines )
(B) K = 1 for tight coupling ( i.e. when two coils are wound on each other).
(C) When the axis of two coils are ⊥ to each other & on different lines K = 0 & this case is called zero coupling.
^Mutual induction (M)
1. Property of a coil due to which it suppress the variations in current in it by inducing a back EMF in the neighbouring coil is called mutual induction. It is measured by a quantity called mutual inductance (M), which is defined as, 
.
2. SI unit of both self & mutual inductance is henry (H).
3. For two long coaxial solenoid wound on same core, 
4. Reciprocity theorem: M12 = M21
^Self induction
1. Property of a coil due to which it suppress the variations in current in it by inducing a back EMF in itself is called self induction. It is measured by a quantity called self inductance (L), which is 
2. For a coil & long solenoid
(a) self inductance, L = A l μm n2
(b) Magnetic energy is, 
(c) Magnetic energy density is, 
3. An inductor (also called a solenoid, or long coil or electromagnet) bent in the form of a coil & made from a thick wire of negligible resisitivity so as to have zero ohmic resistance e. R = 0 is called an ideal inductor or solenoid.
^emf by changing area
Diagram shows a rectangular loop of length L, breadth b, moved towards a region of uniform magnetic field B at a uniform velocity v.
Due to change in magnetic flux with time the emf induced in the loop is, ε = B L v. This causes current 
(clockwise) in loop. Due to current magnetic force 
acts on length. This tends to retard the loop. In order to pull the wire frame with uniform velocity external force 
is to be applied on the loop. The rate at which the applied force does work to maintain the velocity of the wire frame is 
. This work done is actually appearing in the form of electric energy in the loop.
^Lenz rule
Induced EMF produced in a circuit always flows in a direction so as to oppose its cause (i.e. change of magnetic flux).
^Electromagnetic induction
Faraday discovered that a time-varying magnetic field produces an electric field more precisely time varying magnetic flux linked with a circuit induces an electric field in it. This field is non conservative & forms closed loops in the circuit in which it is induced (unlike electrostatic electric field, which never forms closed loop & is conservative). Line integral of this electric field gives emf induced (ε) it lasts as long as the change in magnetic flux continues & is defined as 
(Called Faraday flux rule)
This electric field pushes the charges around the circuit, if the circuit is closed & has say resistance R, a current starts flowing in it, given by 
.
The emf induced is independent of resistance of the circuit but current depends on resistance.
Work done in moving a charge around in induced electric field in a cyclic path is not zero, & W = q ε.
The charge induced doesn’t depend on the rate of change of the magnetic flux, instead is depends on the net change in flux & is 
.
^Commonly used results in electricity & magnetism
| Electricity | Magnetism | |
| Source of field | Static or moving charges | Moving charges |
| SI units | Charge: coulomb (C)Electric field: Newton /coulomb (N/C) | Magnetic pole: ampere meter (Am).Magnetic field is tesla (T) |
| Field lines | Discontinuous: Start at a + ve charge & end at equal -ve charge. | Continuous: Have no start or end & are closed loops. |
| Field due to a mono pole |  |
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| Proportionality constant | 
(SI units) ke = 1 in cgs units |
 in SI unitskm = 1 in cgs units |
| Force on a monopole |  |
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| Potential due to a mono pole |  |
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| Coulomb’s law of two point poles |  |
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| Screening or shielding | Using hollow metallic boxes. | Using ferromagnetic boxes. |
| Gauss’s law |  |
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| Force exerted by field on charge particles |  |
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| Trajectories of charged particles in field | In electric field:
1. Straight line if the angle between electric field & velocity of the charges particle is 00 or 1800 & 2. parabolic if the angle between electric field & velocity of the charges particle is other than 00 & 1800. |
In magnetic field:
1. Straight line if the angle between magnetic field & velocity of the charges particle is 00 or 1800, 2. circular if the angle between magnetic field & velocity of the charges particle is 900. 3. helical if the angle between magnetic field & velocity of the charges particle is other than 00, 900 & 1800. |
| Dipole moment of a dipole of length 2 L |  |
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| Field on axial line of a dipole |  |
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| Field on equatorial of a dipole |  |
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| Field at any point of short dipole |  |
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| Potential on the axial line of dipole |  |
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| Potential at any point of short dipole |  |
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| Force on a dipole placed in a region of uniform field | Force on each pole = qE
Net force on dipole = 0 |
Force on each pole = mB
Net force on dipole = 0 |
| Force on a dipole placed in a non uniform field |  |
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| Torque acting on dipole placed in a region of uniform field |  |
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| Condition for equilibrium of dipole placed in a region of uniform field |  |
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| Potential energy of dipole – field system placed in a region of uniform field |  |
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^Comparative study of Dia, para & ferro
| Property | Diamagnetic | Paramagnetic | Ferromagnetic |
| Physical state | Solid, liquid or gas | Solid, liquid or gas | Crystalline solids only |
| Atomic dipole moments | Zero permanent dipole moment | Non – zero permanent dipole moments but oriented randomly | Non – zero permanent dipole moments but organised in domains |
| Effect of external mag. field | Feebly repelled | Feebly attracted | Strongly attracted |
| A freely suspended rod in a uniform magnetic field | A diamagnetic rod aligns itself normal to field | A paramagnetic rod aligns itself along field | A ferromag. rod quickly aligns itself along field |
| In a non uniform magnetic field | Tend to move slowly from stronger to weaker field. | Tend to move slowly from weaker to stronger field | Tend to move quickly from weaker to stronger. |
Intensity of magnetization  |
Small – ve | Small +ve | Large +ve |
| Relative permeability (μr) | 0 ≤ μr < 1 (slightly) | μr > 1 (slightly) | > 1 Quite large
( ≈ 1012) |
Permeability  |
μ < μ0 | μ > μ0 | μ >>μ0 |
Mag. susceptibility  |
Small – ve (≈ 1) | Small + ve (≈ 1) | Large + ve ( ≈ 1012) |
| B in a medium is | More than in diamagnetic | Less than in a paramagnetic | Much lesser in a ferromagnetic |
| Dependence of χm on H | Independent | Independent | Independent |
| Dependence of χm on H | χ ∝ T0 |  (Curie law) |
 (Curie weiss) |
| Can be explained by | Orbital motion of electrons | Spin motion of e– s (90%) | Domain Theory |
| Transition | No | Para increases (on cooling) | Ferro® para (on heating) |
| Effect of temperature | No effect
(Except Bi at low T) |
Decreases | Decreases
(T=TC, F → P) |
| Examples | People, frogs, bismuth, copper, gold, zinc, silver, Diamond, graphite, mercury, lead, water, hydrogen, nitrogen (at NTP),NaCl, CO2, benzene & all inert gases. | Transition elements, rare earth elements and actinide elements, oxygen gas, air, aluminum, tungsten, titanium, cerium. | Iron, cobalt, nickel, gadolinium, dysprosium, Fe2 O3, alnico and alloys containing these elements. |
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