Simply Lecture

Also called the Faraday law of "electromagnetic induction". The Maxwell third equation has two statements. Statement I:  It states that whenever a magnetic flux link with a circuit changes, then induced electromotive force (emf)  is set up in the circuit. Statement II: The magnitude of induced emf is equal to the rate of magnetic flux linked with the circuit. Integral form: Therefore; $$Induced-emf = - \frac {d\psi_m}{dt}$$ where, $$\psi_m = \int B.ds$$   ......(5) The negative sign is because of Lentz law,  which states that the induced emf set up a current in such a direction that the magnetic effect produced by it opposes the cause producing it. Also, the definition of emf states that the emf is the closed line integral of the non conservative electric field generated by the battery. That is: $$emf = \int E.dL$$ ........(6) Comparing equ(5) and equ(6) we have: $$\int E.dL = -\int_{s} \frac{dB.ds}{dt}$$ ...(7) Differential form Applying Sto...

The Maxwell second law is also called "Gauss law of magnetism". Statement: It states that the total magnetic flux $$\psi_m$$ emerging through a closed surface is zero. Integral form:  $$\psi_m = \int B.ds = 0$$ .......(3) Equ (3)  is the integral form of the Maxwell equation. This equation also proves that the magnetic monopole does not exist. Differential form: Apply Gauss divergence theorem to equ (3). That is: $$\int_{s} B.ds = \int_{v} (\nabla.B) dV$$ Since: $$\int B.ds =0$$ Thus: $$\nabla.B = 0$$ .......(4) Equ(4) is the differential form of the Maxwell second equation.

The Maxwell first equation in electrostatics is called the Gauss law in electrostatics. Statement:  It states that the total electric flux \(\psi_E\) passing through a closed hypothetical surface is equal to \(\frac{1}{\epsilon_0}\) enclosed by the surface. Integral Form: $$\phi_E = \int E.ds = \frac{q}{\epsilon_0}$$ $$\int D.ds = q$$ where, $$D = \epsilon_0 E = displacement-vector$$ Let the change be distributed over a volume v and \(\rho\) be the volume charge density. Hence, $$q = \int \rho dv$$ Therefore; $$\int D.ds = \int_{v} \rho dv$$ .........(1) Equ(1) is the integral form of Maxwell first law Differential form: Apply Gauss divergence theorem to the L.H.S of equ(1) from surface integral to volume integral. $$\int D.ds = \int (\nabla.D)dv$$ Substituting this equation to equ(1) $$\int(\nabla.D)dv = \int_{v} \rho dv$$ As two volume integrals are equal only if their integrands are equal. Thus; $$\nabla.D = \rho v$$ ............(2) Equ(2) is the dif...

What is variable?  A variable is a representation of a value. Let's take for instance, A=40; the representation of 40 is A, so A is called the variable. For storing information,  a variable can be called "containers". Rules for variable  1. Add a $ (dollar sign) in front or before the variable name. For example: $No_of_oranges 2. The PHP cannot begin with numerals; despite the fact of adding the dollar sign ($) in front of the variable name. The variable name must begin with alphabets or underscore sign(_). 3. The PHP variable may contain the following characters: Numerals: (0-9) Alphabets: (A-Z) or (a-z)  Underscore: (_) 4. PHP variables are case sensitive. ie. $No_of_oranges and $NO_OF_ORANGES are different variable 5. Variable name can be any length long. Variable Types: 1. Scalar types: Boolean Integer Float String 2. Compound types: Object Array 3. Special types: Resource  Null Let's take an example: <?php $string...

Syntax  Recall: From our last post we discussed about syntax, but let's take an insight. Below are the opening and closing syntax of a php. Opening tags: <?php <? <script language='php'> Closing tags: ?> ?> (short tag) </script> PHP echo  The echo statement helps in inserting words into a web page. The echo statement is used more often in PHP. A statement can be echoed using the following types: Single Quote Double Quotes Without Quote "here document" method  Let's take a "hello simply lecture" example: <?php echo 'hello simply lecture';  //single quote echo "hello simply lecture"; //double quote echo hello simply lecture; //without quote echo <<<END hello simply lecture END; ?>

What is PHP? PHP stands for "Hypertext processor" and was initially called "personal home page". PHP does not charge users, hence it is free to download and use. PHP is designed for web use as a scripting language and works only with web server. Examples are: Apache, IIS, nginx etc. which means that the PHP script only runs in web servers. It is an HTML-embedded scripting language. Syntax The opening and closing tags of PHP syntax includes: Opening tags: <?php <? <script language='php'> Closing tags: ?> ?> (short tag) </script> Note:  To use syntax 2 of the closing tags, short tags must be turned "on" in php.ini located at the php.ini file. To turn this on use: short_open_tag=on PHP file The extension of PHP file is (.php). The PHP files contains codes from html, css, java script, user text and php code. The method of code execution in PHP is called "sever side code" but when the code is execute...

Before, we start discussing about the work done of an expanding gas, it is advisable to first of all know about the work done of a gas. The work done of a gas is derived as follows: Recall: the work done (w) is given as: $$w = fs$$ ........(1) Where, f = force s = distance But for a gas; work done (w) is given as: $$w = pv$$ .........(2) Where, p = pressure and v = volume During a change of state the work done is written as: $$dw=pdv$$ Adding all the change, we have: $$\int dw = \int_{v_1}^{v_2} pdv$$ .......(3) But, p = constant Therefore, equ (3) becomes: $$w = p \int_{v_1}^{v_2} dv$$ .............(4) Equ(4) is the work done of the gas. Expansion of gas Expansion of gas which is sometimes called "free expansion" is a process in which gas expands into an insulated evacuated chamber. For real gases,  they experience change in temperature but for ideal gases, there is no change in temperature. From the equation: $$p_1v_1 = p_2v_2$$ Where; p1 = initial p...