Electric current (I) & current density (J)
Electric current is the rate at which electric charge crosses a plane. i.e. mathematically, 
Current per unit area is called current density, i.e. mathematically, 
Electric current is scalar, while current density is vector. I & J are parallel to applied E – field.
Kirchoff’s laws
1st or junction rule: Σq = 0 at any isolated junction to conserve charge.
2nd or mesh rule: ΣV = 0 for any closed mesh to conserve energy.
For shown circuit we can write
At jn. A: – q1 + q2 + q3 = 0
Parallel grouping of capacitors
1. Potential difference across all the components connected in parallel is same (i.e. V = constant)
2. Charge is among the various capacitors in accordance with q ∝ C i.e. a capacitor of greater capacitance will get more charge & vice versa.
3. Effective capacitance is is given by, 
Spherical capacitor inner earthed
Suppose a neutral metal sphere radius a is placed concentrically inside a metal shell of radius b having surface charge +q.
If inner sphere a is earthed then charge q/ appears on its surface from earth so that the potential of b becomes zero. i.e.,
Due to earthing & induction the final charge distribution will be
Due to this charge distribution electric field will be
1. E = 0 for r < a (i.e. inside a)
2. 
(radially outward) for a ≤ r ≤ b
3. 
(radially outward) for r > b
Due to earthing potential of a is zero & potential on b due to charge on outer surface of a & inner surface of b get cancelled & final potential on b is
Using C = q/V, capacitance for this system is
The above relation can be expressed as
Isolated spherical conductor
1. Capacitance of an isolated spherical conductor of radius ‘a’ is Cearth = 4 πε0 a
2. As C ∝ a, thus big spheres have more capacitance than small spheres.
3. If the spherical isolated conductor is earthed, then entire charge leaks to earth, making its potential zero & thus C = ∞.
4. For earth capacitance is 
^Type of physical quantities
Physical quantities can be categorized in following four types:
(a) Scalars (b) Vectors (c) Ratios (d) Tensors
Parallel plate capacitor
If the plates X & Y have equal & opposite charges, then charge distribution on plates is as shown in the adjacent drawing. Usually for a parallel plate capacitor we consider this picture.
Let A is the area of each plate, then the charge density of face A, b, c & d are,
Elec. field on the left side (L) of plates, right side of plate (R) & between the plates due to the charge on face a, b, c & d is
Outside the two plates (i.e. in the regions L & R) the electric field due to the charge on the faces a, b, c & d will cancel out, there will no net electric field outside the plates.
Net elec. field between the plates will be 
i.e. electric field due to a capacitor plates of equal & opposite charge is zero outside it & inside is 
which is uniform both in magnitude & direction, (neglecting fringing). Due to this field there will be attractive force between plates, on each plate it will be, 
Due to this electric field the potential difference between the plates X & Y separated by distance d is, 
Capacitance of a PPC is
If the entire space is filled with a dielectric, then ε0 → Kε0 & capacitance becomes
^Dimensionless Variables
Are the physical quantities which have no dimensions but have variable values.
e.g. Angle, Strain, Specific gravity etc.
Field due to charged conductors
Under electrostatic conditions for a conductor of any shape,
Point charge
A body of almost no size is called a point body or discrete body i.e. a sphere of radius R → 0 is a point like body. Both field & potential are not defined on a discrete charge, as r → 0 implies E & V → ∞. Outside the point charge field & potential are
Field of a point charge has following properties
1. radially outward if charge is positive & inwards if it is negative.
2. at finite distance around it, field is spherically symmetric & obeys inverse square law i.e. it is not uniform
3. at infinite distance from the it, field is zero
4. maxi. it the charge is placed in vacuum or air.
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