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**Electric charge and field**

**Electric charge:**

- Intrinsic properties of particles

- It can be Positive or negative in nature.

**Electrically neutral:**Amount of positive and negative charge are same on Particles.

**Electrically Charged:**Amount of positive and negative charge are not same on Particles.

- Particles with the same nature repel each other.

- Particles with opposite nature attract each other.

**Methods of charging:**

**1.By friction:**

- Two bodies will be initially neutral.

- One body rubs with another.

- Finally Opposite charge will appear on both bodies.

**2.By conduction:**

- One will be charged and another neutral.

- Physical contact is required.

- Same types of charges will appear.

- Charge will transfer from one body to another, hence the sum of the charge on bodies will be constant.

**3.Induction:**

- One body will be charge and another will be neutral

- Initially a neutral body would be earthed.

- Keep both bodies closer. i.e: Physical contact is not required.

- Opposite charge induced on the neutral body.

- Charged body will not lose its charge.

**Properties of electrical charge:**

**1.Quantization of charge:**

- Charge on the body is the integer multiple of charge on an electron.

i.e: $Q=n×e$ where n=1,2,.........$e=1.6×10_{−16}$

**2.Conservation of charge:**

- Total charge on an isolated system is constant.

- Isolated system means: the system through its boundary change is not allowed to escape.

**3.Additivity of charge:**

- Total charge on the body is an algebraic sum of total charge located anywhere on it.

- While adding signs taken into consideration.

Q= 2+4+6-5= 7C

**4.Charge is Invariant:**

- Charge does not depend on the speed of the body.

**Coulomb's law:**

Force between point charge is proportional to the product of magnitude of charge and inversely proportional to square of distance between them.

ie, $F_{e}=r_{2}Kq_{1}Q_{2} $

Where, $K=4πϵ_{0}ϵ_{r}1 $$K=9×10_{9}Nm_{2}C_{−2}$$ϵ_{r}=1$ in air

.

**Note:**

- Applicable for point charge only.

- Not applicable for distance less then $10_{−15}$ m.

- Electrostatic force is consevative force.

- Comparatively stronger than gravitational force.

- Coulomb's law obey newton's third law.

**Electric field:**

Space around a charge in which its influence can be felt by any other charged particle.

**Electric field intensity:**Force experienced by test charge in presence of other charge particle.

- Test charge is always considered positive.

- Let a charged particle 'q' is experiencing a force 'F'

**Note:**

- Test charge is always considered small because large magnitudes may disturb the original charge distribution. And then we get electric field disturbed configuration.

- For our convenience we took a magnitude of test charge of 1 C.

**Direction of electric field due to point charge:**

- Positive point charge:

- Negative point charge

**Note:**

- Electric field due to point charge is spherically symmetrical.

- Force experienced by point charge 'q' in electric field 'E',

- Electric field due to system of charge, $E=E_{1}+E_{2}+E_{3}+.........E_{n}$

**Lines of force:**

- Imaginary lines

- Tangent at any point on this line gives direction to the electric field.

**Properties of Electrical lines of forces:**

- Originate from positive charge.

- Converge at negative charge.

- Numbers of lines originating or terminating from charge 'q' C is $q/ϵ_{o}$

- Two lines never cross each other.

- These lines can never be closed loops. ie: originating and converging at same point.

- From surface conductor electrical lines of force start or end normally.

- Tangent on it gives direction of electric field vector.

- Closer lines show more intensity points.

**Electric field from charged body**

- Charged ring

- Infinite line charge

- Uniformly charged disc

- Oppositely charged sheet

**Electric dipole:**

- Two equal and opposite charges at small distance.

- Dipole moment $P=q×2l$

- Direction of dipole moment is from negative charge to positive charge.

- Unit of dipole moment 'Coulomb-metre'

**Electric field intensity due to electrical dipole:**

**Along axial line:**

Direction: Same as direction of dipole vector

**Along equatorial line:**

Direction: Opposite of direction of dipole vector

**At any general point:**

Direction:$tanϕ=21 tanθ$

**Net Force on dipole**

**Due to point charge:**

Force on dipole due to charge = Force on charge due to dipole.

Let, the electric field due to the dipole at a given point of charge is E.Force on charge 'q' due to dipole,

$F_{q}=qE$

Hence, Force on dipole, $F_{d}=−F_{q}=−qE$

**Due to uniform electric field:**

$F_{net}=qE−qE=0N$

**Due to non-uniform electric field:**

**Due to another dipole:**

Where, $F_{12}$ = Force on dipole 1 due to 2.

$E$ = Electric field due to 2 nd dipole.

**Torques on dipole:**

$τ=P×E$

**Electric flux**

- Measure the amount of field line passing through the cross section.
- Electric flux $ϕ=E⋅dS$
**Direction:**- Consider Negative: when flux inter to the surface.
- Consider Positive: when flux leaves the surface.

**Gauss's law:**

- Gives relation between electric field and charge.
- Useful to calculate electric fields due to symmetric charge distribution.

Flux through any closed surface $ϕ=ϵ_{o}q_{inclosed} $

Also, $ϕ=ϕ=E⋅dS=ϵ_{o}q_{inclosed} $

Where, $dS$ Elementary area of gaussian surface.

**Selection of Gaussian surface**

Charge Distribution | Gaussian Surface | Electric field |

Point charge | Spherical | Radial |

Spherical charge | Spherical | Radial |

Linear charge | Cylindrical | Radial |

Planer charge | Planer, Parallel to charged distribution | Normal to the surface |