^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. |
*||gm law of resultant of two vectors
Resultant of two vectors inclined at an angle θ is given by the diagonal of the parallelogram formed by them. If 
are along adjacent sides of a parallelogram 
, then will be the diagonal of the same parallelogram provided 
all have same order. act at an angle θ have, then
c2 = a2 +b2 + 2 ab cosθ [Law of cosine
Cu voltameter
It consists of a glass vessel containing an aqueous solution of CuSO4 as electrolyte & two copper rods as electrodes. Copper sulphate in aqueous solution dissociated as 
.
Due to the applied p.d. the SO2-4 ions drift towards the anode & the Cu2+ ions drift towards the cathode.
The SO2-4 ions on reaching the anode react with Cu atoms of anode to form CuSO4. i.e.
Cu + SO2-4 → Cu2+ SO2-4 + 2 e–
Also the oxidation reaction at the anode is
Cu → Cu2+ + 2e–
These Cu2+ ions dissolve into the solution, while the electrons so released flow towards the positive terminal of the battery via the external circuit. The Cu2+ ions on reaching the cathode get neutralized by the electrons flowing in from the negative terminal of the battery i.e. reduction occurs at the anode, Cu2+ + 2e– → Cu.
The net effect of electrolysis is that one copper atom is deposited at the cathode for each pair of electrons flowing through the connecting wires, thus copper is dissolved from the anode and deposited at the cathode in such a way that the concentration of CuSO4 in the solution remains constant & there is no accumulation of charge any where.
^Accuracy & Precision
The accuracy of a measurement is a measure of how close the measured value is to the true value of the quantity. Precision tells us to what resolution or limit the quantity is measured.
For example, suppose the true value of a certain length is near 3.678 cm. In one experiment, using a measuring instrument of resolution 0.1 cm, the measured value is found to be 3.5 cm, while in another experiment using a measuring device of greater resolution, say 0.01 cm, the length is determined to be 3.38 cm. The first measurement has more accuracy (because it is closer
to the true value) but less precision (its resolution is only 0.1 cm), while the second measurement is less accurate but more precise.
Power transferred theorem
The power transferred by a cell to the load is maximum when R = r & given by
Also then 
Series dielectrics in a capacitor
If three dielectric slabs of thickness t1, t2 & t3, dielectric constants K1, K2 & K3 are placed between the plates of a parallel plate capacitor as shown, then the combination behaves as different dielectrics dividing the spacing are considered as capacitors connected in series.
Capacitance of this is given by
^What is a ratio?
If a physical quantity can be completely described just by knowing its only numerical value, no unit & direction is required, then it is called ratio.
e.g. Strain, Poisson’s ratio, refractive index, relative density, relative permittivity, relative permeability, fine structure constant etc.
Facts
Relative velocity have same dimensions as that of velocity where as relative density is dimensionless.
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