All the Important Formulae that a student should know from….

XII Physics

Unit 1: CHAPTER 1 - ELECTRIC CHARGES AND FIELD

CHAPTER 2 – ELECTROSTATIC POTENTIAL AND

CAPACITANCE

S.

No.

Formula Description

1. Quantization of charge –

Q ne,= ±

Q = total charge (coulomb) e = charge on one electron (coulomb) n = number of electrons

2. The force between two charges q1 and q2 at a distance r from each other

1 22

0

q q1ˆF r

4 r=

πε

�

F = force (newton) q1 and q2 = charges (coulomb) r = distance between charges (meter)

3. Superposition principle -

1 2 3F F F F ......= + + +� � � �

F

�

= net force on the system (newton)

1 2 3F ,F and F� � �

…. = different forces working

on the system (newton)

4. Electric field strength E�

at a point r distance away from a point charge q

20

1 qˆE r

4 r=

πε

�

E�

= Electric field strength (volt / meter) r = distance from a point charge (meter) q = point charge (coulomb)

5. Electrostatic force F�

on a charge

q inside the electric field E�

F�

= q E�

E�

= Electric field strength (volt / meter)

F�

= Electrostatic force (newton) q = point charge (coulomb)

6. Dipole moment p q 2a= ×

p = dipole moment (coulomb meter) q = one of the charges (coulomb) 2a = separation between two charges (meter)

7. Dipole field intensity on axial

line of dipole

1 2 2 20

2prE

4 (r a )=

πε −

�

1E�

= Electric field strength (volt / meter)

p = dipole moment (coulomb meter) 2a = separation between two charges (meter) r = distance of the point from the centre of the dipole (meter)

8. Dipole field intensity on equatorial line of dipole

2 2 2 3 /20

pE

4 (r a )=

πε +

�

2E�

= Electric field strength (volt / meter)

p = dipole moment (coulomb meter) 2a = separation between two charges (meter) r = distance of the point from the centre of the dipole (meter)

9. Dipole field intensity at any point due to a short dipole

2

30

pE 3cos 1,

4 r

1and tan tan

2

= α +πε

β = α

�

E�

= Electric field strength (volt / meter)

p = dipole moment (coulomb meter) r = distance of the point from the centre of the dipole (meter) α= angle which the line joining the point to centre of dipole makes with the axis of dipole

β = the angle at which E

�

is inclined to the

line joining the point the centre of dipole. 10. Torque on dipole inside electric

field is p Eτ = ×�

��

E�

= Electric field strength (volt / meter) p = dipole moment (coulomb meter) τ�

= torque (newton meter)

11. Potential energy of dipole

1 2U pE(cos cos )= − θ − θ

E= Electric field strength (volt / meter) p = dipole moment (coulomb meter)

1θ = initial angle betweenp and E�

�

2θ = final angle between p and E�

�

U = potential energy

12. Flux E. S∆φ = ∆��

E�

= Electric field strength (volt / meter)

ˆS S n∆ = ∆�

= area element (meter2)

φ∆ = flux (weber)

13. Gauss’s law:

φ =0

q

ε

φ = Electric flux through a closed surface

(weber) S = area of closed surface (meter2) q = total charge enclosed by S (coulomb)

14. Application of Gauss’s law: Electric field due to thin infinitely long straight wire of uniform linear charge density

0

1ˆE n

2 r

λ=

πε

�

λ= linear charge density (coulomb /

meter) r = perpendicular distance of the point from the wire (meter)

E�

= Electric field intensity (volt / meter)

n̂ = radial unit vector 15. Electric field due to infinite thin

plane sheet of uniform surface charge density

0

ˆE n2

σ=

ε

�

σ= surface charge density (coulomb /

meter2)

E�

= Electric field intensity (volt / meter)

n̂ = unit vector normal to the plane

16. Electric field due to thin spherical shell uniform surface charge density

20

1 qˆE r

4 r=

πε

�

(r R≥ )

E�

= 0 (r R< )

σ= surface charge density (coulomb /

meter2)

E�

= Electric field intensity (volt / meter) r = the distance of the point from the centre of the shell R = radius of the shell q =total charge on shell

17. Potential at a point due to single charge

V = Potential (volt) q = Point charge (coulomb)

=πε0

1 qV

4 r

r = distance (meter)

18. Potential at a point due to group of N charges

=

=

=πε∑i N

i

i 10 i

q1V

4 r

V = Potential (volt) qi = Point charges (coulomb) ri = Distances (meter)

19. Relation between potential gradient and electric field

= −dV

Edr

E = Electric field (volt / meter) dV

dr = Potential gradient (volt / meter)

20. Electric potential energy of a system of two point charges

=πε

1 2

0 12

q q1U

4 r

U = Electric potential energy (joule) q1 and q2 = Charges (coulomb) r12 = Distance between charges (meter)

21. Electric potential energy of a system of n point charges

≠

=πε

∑i j

i,j,i j0 ij

qq1U

4 r

U = Electric potential energy (joule) qi and qj = Charges (coulomb) rij = Distance between charges (meter)

22. Capacity C = Q / V C = Capacity (farad) Q = Charge (coulomb) V = Potential difference (volt)

23. Capacity of a spherical conductor

= πε0C 4 r

C = Capacity (farad) r = radius (meter)

24. Capacity of a parallel plate capacitor with air as dielectric

ε= 0AC

d

C = Capacity (farad) d = Distance between plates (meter) A = Area of plate (meter2)

25. Capacity of a parallel plate capacitor with insulating medium as dielectric

ε= 0k A

Cd

C = Capacity (farad) d = Distance between plates (meter) A = Area of plate (meter2) k = dielectric constant

26. Capacitors in series Cs = Resultant capacitance (farad)

= + +s 1 2 3

1 1 1 1....

C C C C

C1, C2, C3…= Independent capacitances (farad)

27. Capacitors in parallel

= + + +p 1 2 3C C C C ....

Cp = Resultant capacitance (farad) C1, C2, C3…= Independent capacitances (farad)

28. Energy stored in capacitor

= = =2

21 Q 1E QV CV

2 2C 2

E = Energy stored (joule) Q = Charge (coulomb) C = Capacitance (farad) V = Potential difference (volt)

29. Common potential

+ += =

+ +1 2 1 1 2 2

1 2 1 2

q q C V C VV

C C C C

V = Common potential (volt) V1, V2 = Independent voltages (volt) C1, C2 = Independent capacitances (farad)

30. Loss of energy on sharing charges

−∆ =

+

21 2 1 2

1 2

C C (V V )E

2(C C )

∆E= Energy loss (joule) V1, V2 = Independent voltages (volt) C1, C2 = Independent capacitances (farad)

31. Capacity of a parallel plate capacitor with a conducting slab of thickness t in between the plates

ε=

−0AC

d t

C = Capacity (farad) d = Distance between plates (meter) t = Thickness of slab (meter) A = Area of plate (meter2)

32. Capacity of a parallel plate capacitor with a dielectric slab of thickness t in between the plates

ε=

− −

0AC1

d t(1 )k

C = Capacity (farad) d = Distance between plates (meter) t = Thickness of slab (meter) A = Area of plate (meter2) k = dielectric constant