Board |
SCERT, Kerala |

Text Book |
NCERT Based |

Class |
Plus Two |

Subject |
Physics Notes |

Chapter |
Chapter 1 |

Chapter Name |
Electric Charges and Fields |

Category |
Plus Two Kerala |

## Kerala Plus Two Physics Notes Chapter 1 Electric Charges and Fields

**Simplified Detailed Notes**

**Electrostatics.** It is the study of electric charges at rest.

**Electric charge.** Two types of charges positive and negative were introduced on the basis of frictional electricity produced by rubbing two unlike objects.

**Positive charge.** It is produced by the removal of electrons from a neutral body.

**Negative charge**. It is produced by giving elec-trons to a neutral body.

SI unit of charge is coulomb (C).

**Note.** Proton has +e charge and electron has -e charge.

**Electrostatic induction.** It is illustrated by the following:

**Properties of Charges**

**Conservation of charge.**Total charge of an isolated system is always conserved, i.e., ini¬tial and final charge of the system will be same.**Additive property.**Total charge on a system is equal to the algebraic sum of charges of individual charges present in it.**Quantisation of charge.**Total charge on a body is an integral multiple of fundamental charge ‘e’. i.e., q = ne ; (n = 1, 2, 3 )

**Note:**Like charges repel while unlike charges attract each other.

**Coulomb’s Law.** It states that the electro¬static force of attraction or repulsion between two stationary point charges is directly proportional to the product of magnitude of the two charges and inversely proportional to the square of the distance between them. The direction of this force is along the line joining the two charges.

where £0 is permittivity of free space = 8.854 x 10-12 C2/Nm2

**Dielectric constant or Relative permittivity:** When two charges qt and q2 are placed in any medium other than vacuum, the force between them becomes:

where e is the absolute permittivity of the medium.

where £r is called the relative permittivity of the medium or the dielectric constant of the medium (K).

**Vector form of Coulomb’s Law**

Force on q2 due to q1

This means that the forces exerted by both charges on each other are equal and opposite ie., in accordance with Newton’s third law. Superposition of Electrostatic Forces This principle states that when a number of charges are interacting, the total force on a given charge is equal to the vector sum of the forces exerted on it by all remaining charges.

Note: While adding two vectors which make angle 9 between them, keep this formula in your mind

**Continuous charge distribution**

**Linear charge distribution:** q = λl

where λ = linear charge density.

**Surface charge distribution:** q=σA

where σ= surface charge density.

**Volume charge distribution:** q = ρA

where ρ = volume charge density.

**Electric field intensity** at a point is defined as the force experienced by a unit positive test charge kept at that point. It is given by:

SI unit of electric field intenisty is N/C. It is a vector quantity.

**Electric field intensity due to a point charge**

Electric field at point P is

**Note:** For positive charge E is directed away from the source charge and for negative charge E is directed towards the source charge. Electric field due to a system of charges For addidtion of electric field, we use the same principle of superposition as seen in case of electrostatic forces (vector addition).

Electric field line in an electric field is an imagi-nary smooth curve along which an isolated free positive test charge will move.

**Properties of Electric lines of force.**

- They are continuous with no breaks.
- They start from positive charge and end at negative charge.They do not form closed loops.
- The tangent to a electric field line drawn at any point gives the direction of the ele¬ctric field at that point.
- They do not cross each other.
- They are always normal to the surface of a conductor (in equilbrium condition).
- Equidistant electric field lines represent uniform electric field while electric field lines at different separation represent non uniform electric field.

**Illustration**

**Note:** The nearer the electric field lines, stron-ger is the electric field and farther the electric field lines weaker is the electric field. In the fig-ure electric field strength is greater at P than at Q

**Electric dipole**. It is an arrangement of two equal and opposite charges separated by a small distance.

**Dipole moment (p).** It is the product of magnitude of one of the charges (q) and the sepa-ration between them (2a). .

p = 2aq

SI unit is C-m (coulomb-meter).

**Note:** Its direction is from negative charge to positive charge.

**Electric field at an axial point of a dipole**

**Note:** Direction of electric field at an axial point of the dipole is along dipole axis from negative to positive charge, ie, in the direction of dipole moment.

**Electric field at an equitorial point of a dipole**

**Note:** The direction of electric field at any point on the equatorial line of the dipole will be oppo- j site to the dipole moment.

Torque on a dipole in a uniform electric field

**Derivation:**

Net force on dipole is zero, [(qE) + (-qE)].

But two equal and opposite forces act at two j different points of the dipole. Thus they form j a couple. Hence, there is a net torque on it.

Torque = One of the forces x Perpendicular S distance between the two forces,

**Note:** Torque is maximum when dipole is perpendicular to the electric field and minimum ] when it is held parallel or anti-parallel to the field.

**Area Vector.** It has magnitude equal to the area of the surface and direction of the normal drawn outwards.

**Electric flux.** It is the measure of total number of electric lines of force passing nor¬mally through that area.

For a normal area. It is given by

Thus the total electric flux linked with a closed surface is the surface integral of electric field over it.

**Gauss Law**

It states that the total flux through a closed surface is times the net charge enclosed by the closed surface.

**Applications of Gauss’s Law**

**(i) Electric field due to an infinitely long charged wire.**

Note: Here electric field is inversley proportional to the distance from the line charge.

**(ii) Electric field intensity due to a uniformly charged infinte plane sheet.**

**Note:** Electric field is independent of r.

**(iii) Electric field intensity due to two equally and oppositely charged parallel plane sheets**

**(iv) Electric field intensity due to two posi¬tively charged parallel plane sheets of charge**

**(v) Electric field due to a uniformly charged thin spherical shell.**

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