{"id":4350,"date":"2024-03-03T07:56:58","date_gmt":"2024-03-03T07:56:58","guid":{"rendered":"https:\/\/vartmaaninstitutesirsa.com\/?page_id=4350"},"modified":"2024-03-26T13:14:58","modified_gmt":"2024-03-26T13:14:58","slug":"chapter-2-electrostatic-potential-and-capacitance","status":"publish","type":"page","link":"https:\/\/vartmaaninstitutesirsa.com\/index.php\/chapter-2-electrostatic-potential-and-capacitance\/","title":{"rendered":"Chapter 2 Electrostatic Potential and Capacitance"},"content":{"rendered":"

Chapter 2 Electrostatic Potential and Capacitance<\/h1>\n

Chapter 2 Electrostatic Potential and Capacitance : Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges; equipotential surfaces, electrical potential energy of a system of two-point charges and of electric dipole in an electrostatic field. Conductors and insulators, free charges and bound charges inside a conductor. <\/span>Dielectrics and electric polarization, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance of a parallel <\/span>plate capacitor with and without dielectric medium between the plates, <\/span>energy stored in a capacitor (no derivation, formulae only).<\/span><\/p>\n

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37.\u00a0<\/span>Electric Potential Due to a point charge:-<\/span><\/strong>\u00a0imp<\/sup><\/span><\/strong><\/p>\n

Electrostatic potential at a point is defined as the amount of work done to bring a charge from \u221e to that point against electrostatic force without acceleration<\/span><\/em>.<\/span><\/p>\n

Suppose a test charge q<\/span>0<\/sub><\/span>\u00a0is placed at point A & a charge + q is at point O. Now according to Coulomb\u2019s law the force between the charges is\u00a0<\/span><\/p>\n

F =\u00a0<\/span><\/em>\"\"<\/p>\n

if we move charge from A to B through small distance d<\/span>\ud835\udc65<\/span>\u00a0then small amount of work\u00a0<\/span>\"\"\u00a0may be given<\/span>\u00a0\u00a0\u00a0<\/span><\/p>\n

As<\/span>\u00a0\u00a0<\/span>\"\"\u00a0=\u00a0<\/span>\"\"\u00a0\u00a0<\/span><\/p>\n

\"\"<\/p>\n

= F d<\/span>\ud835\udc65<\/span>\u00a0cos180<\/span>\u00b0<\/span>\u00a0\u00a0<\/span><\/p>\n

= – F d<\/span>\ud835\udc65<\/span><\/p>\n

total work done to move charge from\u00a0<\/span>\u221e\u00a0<\/span>to p is<\/span>\u00a0\u00a0\u00a0<\/span><\/p>\n

W<\/span>\u00a0\u00a0<\/span>=<\/span>\u00a0\u00a0<\/span>–\u00a0<\/span>\"\"\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

= –\u00a0<\/span>\"\"\u00a0d<\/span>\ud835\udc65<\/span>\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

=<\/span>\"\". d<\/span>\ud835\udc65<\/span>\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

=\u00a0<\/span>\"\".d<\/span>\ud835\udc65<\/span><\/p>\n

=<\/span>\u00a0\u00a0<\/span>\"\"\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

=<\/span>\"\"<\/p>\n

=\u00a0<\/span>\"\"<\/p>\n

=<\/span>\"\"\u00a0\u00a0\u00a0\u00a0<\/span><\/strong><\/p>\n

W =<\/span><\/strong>\"\"\u00a0\u00a0<\/span><\/strong>[<\/span><\/strong>\"\"]<\/span><\/strong><\/p>\n

Or<\/span>\u00a0\u00a0\u00a0<\/span>\"\"\u00a0<\/span><\/strong><\/p>\n

Cleary<\/span>\u00a0\u00a0\u00a0\u00a0<\/span>V\u00a0<\/span>\u221d<\/span>\"\"\u00a0\u00a0\u00a0<\/span><\/p>\n

i.e. electric potential varies inversely with distance.<\/span><\/p>\n

At\u00a0<\/span>\"\"\u00a0\u00a0<\/span>, V<\/span>B<\/sub><\/span>\u00a0\u00a0\u00a0<\/span>= 0<\/span>\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

So<\/span>\u00a0\u00a0\u00a0<\/span>\"\"\u00a0= V<\/span>A<\/sub><\/span><\/p>\n

Unit of electrostatic potential is also volt.<\/span>\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

1 volt =\u00a0<\/span>\"\"\u00a0<\/span><\/p>\n

= 1 NmC<\/span>-1<\/sup><\/span>\u00a0\u00a0\u00a0<\/span><\/p>\n

= 1 JC<\/span>-1<\/sup><\/span><\/p>\n

i,e\u00a0<\/span>\u00a0<\/span><\/em>electrostatic potential at a point is said to be one volt if one joule is the amount of work done to move one coulomb charge from \u221e to that point against electrostatic<\/span><\/em>\u00a0force without acceleration.<\/span><\/em><\/p>\n

Electrostatic potential difference:-<\/span><\/strong><\/p>\n

\"\"Suppose a point charge q<\/span>0<\/sub><\/span>\u00a0is placed at point B in the field of any other charge +q then work done to move a charge from B to A is given by\u00a0<\/span><\/p>\n

\"\"\u00a0= V<\/span>A<\/sub><\/span>\u00a0-V<\/span>B<\/sub><\/span>\u00a0<\/span><\/p>\n

= V<\/span>BA<\/sub><\/span><\/p>\n

Hence Electrostatic Potential difference may be defined as the amount of work done to move a unit +ve charge from one point to other point again the electrostatic forces without acceleration.<\/span><\/em><\/p>\n