*Geometrical Meaning of integration is called Integral or primitive of y w.r.t. x or anti-differentiation. Here, ydx is area of elementary rectangular strip of thickness dx. Thus gives the total area bounded by the all the elementary strips of the curve represented by the function y = f (x) with the x-axis between the limits […]
Electric dipole 1. On axial line: 2. On eq. line: 3. At center: 4. Following diagram shows variation of electric field with distance on axial line of dipole. 5. 6. For short dipole (a) On axial line: (b) On equatorial line: (c) Any point: directed at with Ex. (d)
*Integral calculus Integration is the reverse process of differentiation, thus also called anti-differentiation. Suppose we have a function g (x) whose derivative. The function g (x) is known as the indefinite Integral of f (x) and is denoted as: 1/d is usually abbreviated by the symbol ∫ (called integral), so one can write ∫ f […]
Equipotential surfaces An equipotential surface is an imaginary surface on which every point has one and the same value of electric potential. It can be curved or plane surfaces. No work is done in moving any charge over an EPS. Electric field is always ⊥ to EPS. EPS tells us about direction of electric field. […]
*Maxima & minima
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, […]
^Partial derivatives Let y = f (u, v, w), then ∂y/∂u means partial derivative y w.r.t. u i.e. differentiating y w.r.t. u, keeping v & w constants. Similarly ∂y/∂v means taking partial differentiation of y w.r.t. v, keeping u & w constants.
Potential energy of point charges 1. For a system of two point charges 2. For a system of three point charges 3. 4. For a stable system U is minimum, its first derivative w.r.t. position (= – F) is zero & its second derivative w.r.t. position is +ve.
^Rules of differentiation Following table displays some commonly used differentials in physics.
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 […]
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