^Capacitor
Capacitor
A capacitor is an arrangement of two conductors (called plates) separated from each other by a dielectric medium & used to trap (or store) electric energy in the form of electric field between its plates.
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^Potential due to concentric spheres
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.
^E & V due to uniformly charged sphere
E & V due to uniformly charged sphere
Charge on a insulated sphere of uniform volume charge density r & radius R is 
,
Charge on a spherical insulated shell or a conducting sphere of uniform surface charge density s & radius R is, Q = σ 4 πR2
Using Gauss law we can write
^Advantages of SI system
^Advantages of SI system
Following are the advantages of SI system:
Coherent: SI system of units is coherent. i.e. any unit can be derived by simply dividing & multiplying from any seven fundamental units & two basic units.
Rational: For one physical quantity only one unit is used.
Absolute: Use of ‘g’ is avoided.
Metric: The use of multiples & submultiples is allowed. Accepted universally: As SI system can be easily reproduced, compared & time invariant.
*Fundamental quantities
*Fundamental quantities
Seven physical quantities have been chosen as fundamental or base quantities these are length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity. Units of base quantities are called base units or fundamental units. Fundamental or base quantities are also known as the seven dimensions of the world.
^Electric flux
Electric flux
1. Electric flux (ΦE) linked with a surface (flat or curved) gives us an idea of the total number of electric field lines passing normally through that surface.
2. Electric flux is defined as the surface integral of the electric field inked with that surface i.e.
Here θ is the angle between electric field vector & area vector (
i.e. an area vector conventionally directed normally outwards to the area under consideration).
3. SI unit of flux: Weber (Wb)
4. CGS unit of flux: Maxwell (Mx)
5. Conversion: 1Wb = 10 8 Maxwell = 1Vm
6. Being dot product, electric flux is a scalar quantity.
7. Maximum value of flux = ± E S
8. Minimum value of flux = 0 (when θ = π/2)
9. If θ is acute flux is + ve & called leaving.
10. If θ is obtuse flux is – ve & called entering.
^Finite line charge
Finite line charge
The above result is valid even if the wire is bent to form an arc as shown.
^Electric dipole in uniform electric field
Electric dipole in uniform electric field
Consider an electric dipole in a region of uniform electric field
1. Net force on the dipole for any position is zero.
2. Torque acting on the dipole is 
.
3. Torque acts except for the positions when the dipole moment vector & electric field vector are collinear.
4. Total work done by us in rotating the dipole in a uniform electric field is from angle θ1 to θ2 is
W = pE (cos θ1 – cos θ2)
5. The potential energy of an electric dipole placed in a uniform electric field is 
6. A dipole placed in a non uniform electric field experiences both force and torque.
7. Force on a dipole placed in shown non uniform electric field is 
^Electrostatic potential (V)
Electrostatic potential (V)
Electrostatic potential energy per unit victim charge is called electrostatic potential i.e. 
using this result & F = q E, LCF can be expressed as 
.
If a charge particle is moved from ∞ → P, then the above relation can be expressed as 
Choice of potential is arbitrary & matter of Convenience, usually we assume V = 0 at infinity.
Bothe field & potential are high when observation point is near a positive charge. Whereas near a negative charge field is high & potential is low.
^Partial derivatives
^Partial derivatives
Let y = f (u, v, w), then ∂y/∂u means partial derivative y w.r.t. u i.e. differentiating y w.r.t. u, keeping v & w constants. Similarly ∂y/∂v means taking partial differentiation of y w.r.t. v, keeping u & w constants.
