*The Seven Fundamental Quantities
*The Seven Fundamental Quantities
Posts
^Gaussian surface
Gaussian surface
- To find electric field due to a charge configuration using Gauss’s law we draw an imaginary closed surface around that charged distribution.
- Gaussian surfaces are normal to electric lines of & symmetric to the charge enclosed such that electric field at every point of the Gaussian surface due to that charged distribution is same.
- Gaussian surfaces are spherical for point charges or spherical distribution of charges & cylindrical for linear and planar distribution of charge.
- Only those charges which lie inside the Gaussian surface are considered & that located outside have no contribution in the flux.
- Discrete charges on the surface of the -Gaussian surface are not considered (as electric field at the location of a discrete charge is not defined) but continuous charges can be considered.
^For infinite line charge
For infinite line charge
Both α & β will approach to 900 & E becomes
*Integral calculus
*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 (x) dx = g (x) + c
Here c is called constant of integration. Its value is arbitrary and can be calculated form the information given in the problem.
Integral of the form 
is called definite integral. Here x = a & x = b are called limits of integration. x = a is called lower limit & x = b is called upper limit. If limits are not given, then the integration is called indefinite integration.
Definite integral is a number. Indefinite integral has no limits; it is a function. No integration constant is required in the final answer in definite integrals. Following examples explain how one can derive integration from differentiation.
^Charge is source of field
Charge is source of field
- An electric charge at rest produces only electric field around it.
- An electric charge moving with uniform velocity produces both electric and magnetic fields around it but radiates no energy.
- An accelerated charge produces both electric and magnetic fields around it as well as radiates energy in the form of electromagnetic waves.
*Graph of exponential functions
*Graph of exponential functions
Functions y = ax, a < 1 & y = a– x, a > 1 are exponentially decreasing. Functions y = ax, a > 1 & y = a– x, a<1 are exponentially increasing.
The y intercept of the function y = ax is point (0, 1). If a = e (2.71828) then y = ex is called natural exponential function.
*Up or down parabola
*Up or down parabola
A quadratic of the form y = ax2 + bx + c represents an upward or a downward parabola, it can also be expressed by the following function
(x – u)2 = L (y – v)
L= +ve for upward parabola & L = – ve for a downward parabola.
*Trigonometric functions
*Trigonometric functions
We know following values for sinθ & cosθ.
Using these values we can plot the following graphs:
Note the function y = sinx completes one cycle at 3600 where as y = sin2x completes it at 1800 & at
y = sinx/2 completes it at 7200.
*Laws of log
*Laws of log
Examples
- log 3587 = 3.5548
- log 358.7 = 2.5548
- log 35.87 = 1.5548
- log 3.587 = 0.5548
- antilog 0.5220 = 3.327
- antilog 1.5220 = 33.27
- antilog 2.5220 = 332.7
*Componendo & dividendo
*Componendo & dividendo
