Electrostatic potential (V)

Electrostatic potential energy per unit victim charge is called electrostatic potential i.e. using this result & F = q E, LCF can be expressed as .

If a charge particle is moved from ∞ → P, then the above relation can be expressed as

Choice of potential is arbitrary & matter of Convenience, usually we assume V = 0 at infinity.

Bothe field & potential are high when observation point is near a positive charge. Whereas near a negative charge field is high & potential is low.

Work done by a electrostatic force

Work done by a electrostatic force ‘F’ in moving a point charge ‘q’ from a point A to point a point B situated in conservative electrostatic field

1. is path independent

2. depends only upon the initial & final positions

3. is equal to loss of potential energy of the point charge between these positions. i.e.

4. zero for a cyclic path.

*Ellipse

An ellipse is a closed curve like a circle. An ellipse may be drawn by choosing two points F₁ and F₂, each of which is a called a focus, and then drawing a curve through points for which the sum of the distances PF₁ and PF₂, respectively, is a constant.

If the center of ellipse is at point origin

Note if a = b, ellipse becomes a circle of radius a.

Area of ellipse = πab

*Mean of n terms

If x₁, x₂, _ _ _ _ _ _ _ _ _ , x_n be n quantities then their

If A, G and H be A.M., G.M. and H.M. between two numbers, then

(a) A ³ G ³ H,(b) G² = A .H

Series