12th physics electric charges and field-Electric Field Electric Field Lines Continuous Charge Distribution

Electric Field Electric Field Lines Continuous Charge Distribution

Electric Field − It is the space around a charge, in which any other charge experiences an electrostatic force.

Electric Field Intensity − The electric field intensity at a point due to a source charge is defined as the force experienced per unit positive test charge placed at that point without disturbing the source charge.

Where,

→ Electric field intensity

Force experienced by the test charge q₀

Its SI unit is NC⁻¹.

Electric Field Due To a Point Charge

We have to find electric field at point P due to point charge +q placed at the origin such that 

To find the same, place a vanishingly small positive test charge q₀ at point P.

According to Coulomb’s law, force on the test charge q₀ due to charge q is

If is the electric field at point P, then

The magnitude of the electric field at point P is given by,

Representation of Electric Field

Electric Field Due To a System of Charges

Consider that n point charges q₁, q₂, q₃, … q_n exert forces on the test charge placed at origin O.

Let be force due to i^th charge q_i on q₀. Then,

Where, r_i is the distance of the test charge q₀ from q_i

The electric field at the observation point P is given by,

If  is the electric field at point P due to the system of charges, then by principal of superposition of electric fields,

Using equation (i), we obtain

Electric Field Lines

An electric line of force is the path along which a unit positive charge would move, if it is free to do so.

• Properties of Electric Lines of Force

• These start from the positive charge and end at the negative charge.
• They always originate or terminate at right angles to the surface of the charge.
• They can never intersect each other because it will mean that at that particular point, electric field has two directions. It is not possible.
• They do not pass through a conductor.
• They contract longitudinally.
• They exert a lateral pressure on each other.

• Representation of Electric Field Lines

• Field lines in case of isolated point charges

• Field lines in case of a system of two charges

Continuous Charge Distribution

• Linear charge density − When charge is distributed along a line, the charge distribution is called linear.

Where,

λ → Linear charge density

q → Charge distributed along a line

L → Length of the rod

• Surface charge density

Where,

σ → Surface charge density

q → Charge distributed on area A

• Volume charge density

Where,

δ → Volume charge density

V → Volume of the conductor

q → Charge on conductor