Series grouping of capacitors
1. Charge on all the components connected in series is same (i.e. q = constant).
2. Potential difference is divided among the various capacitors in accordance with 
e. a capacitor of smaller capacitance will get more potential difference & vice versa.
3. Effective capacitance is given by, 
PPC with a metal slab in plates
If a metal slab (dielectric constant K = ∞), thickness t < d is placed between the plates of a PPC, then due to the electric field 
between the capacitor plates the dielectric gets polarized & an electric equal to E0 is induced in it, as a consequence net electric field in dielectric is found to be zero i.e. Enet = 0.
Due to this field electric field net potential difference across the capacitor plates becomes 
Using C = q/V, capacitance of capacitor becomes 
If the conducting slab occupies the entire space available between the plates of capacitor i.e. when t =d & K = ∞, then C = ∞
Comparing (a), (b) & (c) we can say
CDS > CCS > Co
If both magnitude and direction are required to completely described a physical quantity, then it is called a vector. A vector quantity is represented by putting on arrow above it or by bold letter e.g. it Q is vector then we represent it as or Q. if a quantity can have any direction it is called polar. If its direction is along axis only then called axial.
^Dimensionless Quantities
Strain, angle, solid angle, all Trigonometric ratios, all real numbers, logarithmic functions, exponential functions, Poisson’s ratio, refractive index, relative density, relative permittivity, relative permeability, fine structure constant etc. have no dimensions.
Capacitance
1. Capacitance of a system is a measure of the its capacity to hold charge for a given potential difference.
2. Capacitance can be defined as
3. Capacitance is defined even if a capacitor is neutral.
4. SI unit of capacitance is Farad (F).
5. 1F = 1 C V – 1 = 9 x 1011 stat farad.
6. Farad is a too big unit. Practical capacitors are of the order of mF, nF & pF etc.
7. Generally the two plates have equal and opposite charges. Even if, we give different charges to the plates then the inner surfaces facing each other posses equal and opposite charges.
8. The plates are separated by a distance much smaller than dimensions of a capacitor.
Potential due to concentric spheres
Consider two identical concentric spheres of radii R1 & R2 carry charges q1 & q2 respectively as shown in the diagram. Then total potential on A & B will be equal to sum of potentials due to charge on A & B & given by
The potential diff. between two surfaces is
From above relation we can say
1. The potential difference is independent of the charge on the outer sphere.
2. 
3. When the two conductors are joined by a thin wire, their potentials becomes same i.e. potential difference between them becomes zero. This is possible only when q1 is zero i.e. actually this will happen only when the entire charge on A moves to sphere B.
4. If q1 is negative, even then entire charge on A moves to sphere B, as we know negative charge moves from low to high potential.
^Rules for writing units
In calculations the prefix is attached with the numerator and not with the denominator.
*The Seven Fundamental Quantities
Gauss’s law
1. According to Gauss’s law the electric flux through any arbitrary closed surface in a medium is equal to the total charge enclosed by the that surface divided by the permittivity of that medium. i.e. 
2. If medium is air or vacuum, then 
3. Gauss’s law is based on the inverse square dependence on distance contained in the Coulomb’s law. Any violation of Gauss’s law will indicate departure from the inverse square law.
4. Using Gauss law we can say no. of electric line of force originating or terminating on a charge of q coulomb is equal to q/ε0.
Finite line charge
The above result is valid even if the wire is bent to form an arc as shown.
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