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It is a branch of physics that deals with the phenomena and properties of stationary or slowmoving electric charges with no acceleration.
The property associated with matter due to which it produces and experiences electric and magnetic fields.
It states that the electrostatic force of attraction or repulsion between two charged bodies is directly proportional to the product of their charges and varies inversely as the square of the distance between the two bodies.
Here,
K = 1/(4πε_{0}) = 9×10^{9} Nm^{2}C^{2} (in free space)
The relative permittivity (ε_{r}) of a medium is defined as the ratio between its permittivity of the medium (ε) and the permittivity (ε_{0}) of the free space.
i.e. ε_{r} = ε/ε_{0}
The force on charge q_{1} due to q_{2} is,
If q_{1}q_{2}>0, R.H.S is positive but if q_{1}q_{2}<0, a negative sign from q_{1} or q_{2} will changeto. The relation will again be true, since, in that case, have the same directions.
The total force on a given charge is the vector sum of all the individual forces exerted by each of the other charges.
The dielectric constant (ε_{r}) of a medium can be defined as the ratio of the force between two charges separated by some distance apart in free space to the force between the same two charges separated by the same distance apart in that medium.
i.e. ε_{r }= ε/ε_{0} = F_{1}/F_{2}
Here, F_{1} and F_{2} are the magnitudes of the force between them in free space and in a medium respectively.
The strength of an electric field is measured by the force experienced by a unit positive charge placed at that point. The direction of the field is given by the direction of motion of a unit positive charge if it were free to move.
For positive source charge, the electric field is radially outward, whereas, for negative source charge, the electric field is radially inward.
E = [Newton/Coulomb] or [Joule/(Coulomb) (meter)]
An electric line of force is defined as the path, straight or curved, along which a unit positive charge is urged to move when free to do so in an electric field. The direction of motion of the unit positive charge gives the direction of the line of force.
Electric flux for a surface placed in an electric field is the sum of dot product ofandfor all the elementary areas constituting the surface.
It states that, for any distribution of charges, the total electric flux linked with a closed surface is 1/ε_{0} times the total charge with in the surface.
The space around an electric charge in which its influence can be felt is known as the electric field. The electric field intensity at a point is the force experienced by a unit positive charge placed at that point.
Electric Field Intensity (E) = q/[4πεd^{2}]NC^{1}
E = (1/4πε_{0}) (q/r^{2})
E = λ/2πε_{0}r
The direction of electric field E is radially outward for a line of positive charge.
 Outside Point: E_{out }= (1/4πε_{0}) (q/r^{2})
 Inside Point: E_{in} = 0
 Point at outside (r > R): E = (1/4πε_{0}) (q/r^{2})
 Point at inside (r < R): E = (1/4πε_{0}) (qr/R^{3})
Here, q is the total charge.
 Outside Point: E_{out} = (1/4πε_{0}) (Q/r^{2})
 Inside Point: E_{in} = (1/4πε_{0}) (Q_{r}/R^{3})
 On the Surface: E_{surface} = (1/4πε_{0}) (Q/R^{2})
Here, Q is the total charge
 Outside the cylinder: E = λ/(2πε_{0}r)
 Inside the cylinder: E = 0
 Outside the cylinder: E = λ/2πε_{0}r
 Inside the cylinder: E = ρr/2ε_{0}
E = σ/2ε_{0}
_{}
 Electric field at points outside the charged sheets: E_{P} = E_{R} = 0
 Electric field at a point in between the charged sheets: E_{Q} = σ/ε_{0}
E = σ/2ε_{0}
This signifies, the electric field near a charged sheet is independent of the distance of the point from the sheet and depends only upon its charge density and is directed normally to the sheet.
E= σ/ε_{0}
P_{elec }= (1/2 ε_{0}) σ^{2}
An electric dipole is defined as a couple of opposite charges q and –q separated by a distance d.
Dipole moment () of an electric dipole is defined as the product of the magnitude of one of the charges and the vector distance from negative to positive charge.
(a) At any point on the axial line:
(b) At a point on the equatorial line (perpendicular bisector):
(c) At any point:
= pE sinθ
Here, p is the dipole moment and θ is the angle between the direction of dipole moment and electric field E.
Electric potential, at any point, is defined as the negative line integral of the electric field from infinity to that point along any path.
The potential difference, between any two points, in an electric field, is defined as the work done in taking a unit positive charge from one point to the other against the electric field.
W_{AB} = q [V_{A}V_{B}]
So, V = [V_{A}V_{B}] = W/q
V = (1/4π ε_{0}) (q/r)
V = (1/4π ε_{0}) [q_{1}/r_{1} + q_{2}/r_{2} + q_{3}/r_{3}] = V_{1}+V_{2}+ V_{2}+….
Common potential, V = (1/4π ε_{0}) [(Q_{1}+Q_{2})/(r_{1}+r_{2})]
q_{1 }= r_{1}(Q_{1}+Q_{2})/(r_{1}+r_{2}) = r_{1}Q/ r_{1}+r_{2}
q_{2} = r_{2}Q/ r_{1}+r_{2}
q_{1}/q_{2} = r_{1}/r_{2} or σ_{1}/ σ_{2} = r_{1}/r_{2}
V (r,θ) = qa cosθ/(4πε_{0}r_{2)} = p cosθ/(4πε_{0}r_{2)}
If n drops coalesce to form one drop, then,
W = U = 1/(4πε_{0}) (q_{1}q_{2}/r_{1}_{2}) = q_{1}V_{1}
W = U = (1/4πε_{0}) (q_{1}q_{2}/r_{12} + q_{1}q_{3}/r_{13 }+ q_{2}q_{3}/r_{23})
Potential energy of an electric dipole, in an electrostatic field, is defined as the work done in rotating the dipole from zero energy position to the desired position in the electric field.
K. E = 1/2 mv^{2} = eV
Conductors are those substances through which electric charge flow easily.
Insulators (also called dielectrics) are those substances through which electric charge cannot flow easily.
The capacity of a conductor is defined as the ratio between the charge of the conductor to its potential.
C = Q/V
C = 4πε_{0}r
A capacitor or a condenser is an arrangement that provides a larger capacity in a smaller space.
C_{air }= ε_{0}A/d
C_{med} = Kε_{0}A/d
Here, A is the common area of the two plates and d is the distance between the plates.
C = ε_{0}A/[dt+(t/K)]
Here d is the separation between the plates, t is the thickness of the dielectric slab, A is the area and K is the dielectric constant of the material of the slab.
If the space is completely filled with dielectric medium (t=d), then, C = ε_{0}KA/ d
 C_{air} = 4πε_{0}R
 C_{med} = K (4πε_{0}R)
 When outer sphere is earthed:
C_{air }= 4πε_{0} [ab/(ba)]
C_{med }= 4πε_{0 }[Kab/(ba)] When the inner sphere is earthed:
C_{1}= 4πε_{0} [ab/(ba)]
C_{2} = 4πε_{0}b
Net Capacity, C '=4πε_{0}[b^{2}/ba]
Increase in capacity, ΔC = 4π ε_{0}b
It signifies, by connecting the inner sphere to earth and charging the outer one we get an additional capacity equal to the capacity of the outer sphere.
 C_{air} = λl / [(λ/2π ε_{0}) (loge b/a)] = [2πε_{0}l /(loge b/a) ]
 C_{med} = [2πKε_{0}l /(loge b/a) ]
W = ½ QV = ½ Q2/C = ½ CV2
U = ½ ε_{0}E^{2} = ½ (σ^{2}/ ε_{0})
This signifies the energy density of a capacitor is independent of the area of plates and the distance between them so, the value of E does not change.
 C = C_{1}+C_{2}+C_{3}+…..+C_{n}
The resultant capacity of a number of capacitors, connected in parallel, is equal to the sum of their individual capacities. V_{1}= V_{2}= V_{3} = V
 q_{1} =C_{1}V, q_{2} = C_{2}V, q_{3} = C_{3}V
 Energy Stored, U = U_{1}+U_{2}+U_{3}
 1/C = 1/C_{1} + 1/ C_{2} +……+ 1/C_{n}
 The reciprocal of the resultant capacity of a number of capacitors, connected in series, is equal to the sum of the reciprocals of their individual capacities.
 q_{1 }= q_{2} = q_{3} = q
 V1= q/C_{1}, V_{2}= q/C_{2}, V_{3}= q/C_{3}
 Energy Stored, U = U_{1}+U_{2}+U_{3}
(a) F = ½ ε_{0}E^{2}A
(b) F = σ^{2}A/2ε_{0}
(c) F=Q^{2}/2ε_{0}A
F = (Q^{2}/2C^{2}) (dC/dx) = ½ V^{2 }(dC/dx)
V = [C_{1}V_{1}+ C_{2}V_{2}] / [C_{1}+C_{2}] = [Q_{1}+Q_{2}]/ [C_{1}+C_{2}]
ΔQ = [C_{1}C_{2}/C_{1}+C_{2}] [V_{1}V_{2}]
ΔU = ½ [C_{1}C_{2}/C_{1}+C_{2}] [V_{1}V_{2}] ^{2}
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