^Also dimensionally:
Example of LR circuit
Let at t = 0, switch S is closed.
(a) Just on closing switch means t = 0. At this time inductor offers infinite resistance, thus I = 0 and 
(b) A long time after closing switch means at t = ∞. At this time it offers no resistance (as current in inductor attains a maxima), in other words entire current will pass through inductor, hence at t = ∞, I2 = 0 and 
^Current in LR – circuit
An ideal inductor has no ohmic resistance (i.e. R = 0) it has only reactance (i.e. XL ≠ 0). However no inductor is ideal, every inductor can be assumed as series combination of L & R . When such an inductor is connected is connected to a battery (e.g. on throwing switch towards) a current increases exponentially in the outer loop from 0 to become maximum in accordance with the relation 
Due to increase in current voltage across the resistor increases in accordance with the relation 
As the total voltage across the LR combination is always fixed & equal to battery voltage, thus the increase in voltage across the resistor implies a decrease in voltage across the inductor. This is described by the function 
.
On throwing switch towards B current decreases exponentially in the outer loop from maximum to become 0 in accordance with the relation 
^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
^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. |
Declination (θ)
Since the line joining the magnetic poles is titled with respect to the geographic axis of the earth, the magnetic meridian at a point makes angle with the geographic meridian. This angle between the true geographic north and the north shown by a compass needle at which the needle stays in equilibrium in magnetic meridian is called the mag. declination or simply declination.
The declination is greater at higher latitudes and smaller near the equator. The declination in India is small, it being 0º41′ E at Delhi and 0º58′ W at Mumbai. This means a compass needle would deflect towards east by 0 degrees & 41 minute at Delhi & towards west by 0 degrees & 58 minute at Mumbai. As both angles are almost 00, Thus, we can say, at both these places a magnetic needle shows the true north quite accurately.
Properties of a magnet
1. The pole strength ‘m’ of a magnet depends upon the nature of material of a magnet, its state of demagnetization & area of cross section of the magnet but is independent of any bend in the magnet.
2. For a bar magnet 
3. On cutting a magnet in two identical pieces longitudinally (along the length) the pole strength of each part is halved as a result the dipole moment of each part becomes half.
4. On cutting a magnet in two identical pieces transversally (normal to length) the dipole moment of each part becomes as length of each part is halved.
5. A flexible magnet of length L, pole strength m & dipole moment M is bent into a semi circle. The dipole moment of this semicircle will be 
.
6. Demagnetization can be due to heating, hammering, passing AC through an electromagnet, applying demagnetizing field (i.e. a magnetic field in the reverse direction), aging.
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