In electrostatics we deal with the electric effects of charges at rest.<\/p>\n\n\n\n
Electric charge<\/a> can be defined as is the intrinsic characteristic that is associated with fundamental particles due to which they produce and experience electrical and magnetic effects. Charges are of two types<\/p>\n\n\n\n The figure given can give you the brief overview of what electric charge is all about<\/p>\n\n\n\n Always note that any material or body in its normal condition is electrically neutral<\/p>\n\n\n\n A body can be charged either by friction, conduction or by induction<\/p>\n\n\n\n If we pass a comb through hairs, comb becomes electrically charged and can attract small pieces of paper. Many such solid materials are known which on rubbing attract light objects like light feather, bits of papers, straw etc.<\/p>\n\n\n\n So the phenomenon of production of charges in material or body due to friction ,as in case of above examples, is called frictional electricity<\/em>.<\/p>\n\n\n\n Phenomenon of charge transfer where a charged body is placed in contact with another body so that transfer of electrons takes place from one body to another is called charging by conduction.<\/p>\n\n\n\n Electrostatic induction is a redistribution of electrical charge in an object, caused by the influence of nearby charges.In the presence of a charged body, an insulated conductor develops a positive charge on one end and a negative charge on the other end.<\/p>\n\n\n\n Conductors allow large scale movement of electric charge through them, insulators do not. In metals the mobile charges are electrons; in electrolytes both positive and negative ions are mobile.<\/p>\n\n\n\n The electric force exerted on each other by two point charged $q_1$ and $q_2$ , separated by distance $r$, are proportional to the product of $q_{1}q_{2}$, and inversely proportional to the square of the distance between them. they act along the line joining the two charges. These forces are attractive if the charges involved are unlike charges and repulsive if the charges involved are like charges. Mathematically,<\/p> $F\\propto \\frac{q_{1} q_{2}}{r^2}$ or $F=k \\frac{q_{1} q_{2}}{r^2}$<\/p><\/blockquote>\n\n\n\n Here $k=\\frac{1}{4\\pi \\epsilon_{0}}=8.98755\\times 10^{9}Nm^{2}C^{-2}$ is the constant of proportionality.<\/p>\n\n\n\n Electric forces<\/a> exerted by two charges on each other are equal in magnitude and opposite in direction.<\/p>\n\n\n\n Electrostatic force of interaction between two point charges is independent of the presence of other charges. F<\/strong> = F12<\/sub><\/strong> + F13<\/sub><\/strong> + ……………………………. F1n<\/sub><\/strong><\/p>\n\n\n\n Where F12<\/sub><\/strong> is force on q1<\/sub> due to q2<\/sub> and F13<\/sub><\/strong> is force on q1<\/sub> due to q3<\/sub> and so on.<\/p>\n\n\n\n To have a look at Coulomb’s Law<\/a> at a glance have a look at the concept map given below<\/p>\n\n\n\n Electric field is the region surrounding an electric charge or a group of charges in which another charged particle experiences a force of attraction or repulsion.<\/p><\/blockquote>\n\n\n\n Theoretically electric field extends up to infinity but practically but practically electric field is not detectable beyond a certain distance.<\/p>\n\n\n\n Some Points about Electric field can be revised using the following concept map<\/p>\n\n\n\n It is important to note that:-<\/p>\n\n\n\n Important properties of lines of forces<\/strong><\/p>\n\n\n\n Definition:- <\/strong><\/em><\/span><\/p>\n\n\n\n In electrostatics electric potential at any point say $P$ is defined as the work done in taking a positive charge from a reference point (generally taken at infinity) to that point $P$ in the presence of electric field.<\/p><\/blockquote>\n\n\n\n Important Points<\/strong><\/p>\n\n\n\n Electric potential energy of a test charge at any point in the electric field is the work done against the electric forces to bring the charge from infinity to point under consideration. Mathematically , potential energy of test charge q’ at any distance r from charge q is given by Full and detailed notes on Electric potential can be read by following this link<\/a><\/p>\n\n\n\n <\/p>\n Electric dipole is a set of two equal and opposite charges that are separated by small finite distance. On axis of the dipole<\/strong> $\\tau =\\vec{p}\\times \\vec{E}$ It states that total electric flux through a closed surface is equal to $\\frac{1}{\\epsilon_{0}}$ times the net charge $q$ enclosed by the surface i.e.,<\/p>\n\n\n\n $\\int \\vec{E} \\cdot d\\vec{s}=\\frac{q}{\\epsilon_{0}}$<\/p>\n\n\n\n where $d\\vec{s}$ is an element of area; the direction of each element $d\\vec{s}$ of $\\vec{s}$ is along the outward drawn normal to the surface at every point.<\/p>\n\n\n\n For more notes and study material on Gauss’s Law you can visit this link<\/a> and follow on from there.<\/p>\n\n\n\n I have already made a pdf document on the summary of this chapter and I will be providing the download link below.<\/p>\n\n\n\n For more detailed notes on capacitance follow this link<\/a><\/p>\n\n\n\n![\"Concept](\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2015\/08\/electric-charge-1024x434.png\")
<\/a>How to charge a body<\/h2>\n\n\n\n
Charging by friction<\/h3>\n\n\n\n
Charging by conduction<\/h3>\n\n\n\n
Charging by induction<\/h3>\n\n\n\n
Properties of electric charge<\/h3>\n\n\n\n
Coulomb’s Law<\/h2>\n\n\n\n
Principle of superposition<\/h3>\n\n\n\n
If a system of charges has n number of charges say q1<\/sub>, q2<\/sub>, ……………….., qn<\/sub>, then total force on charge q1<\/sub> according to principle of superposition is<\/p>\n\n\n\n![\"Electrostatics](\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2015\/08\/force_charge.png\")
<\/a>Remember these points<\/span><\/em><\/strong><\/pre>\n\n\n\nElectrostatic Field<\/h2>\n\n\n\n
![\"Electrostatics:-](\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2015\/08\/electric-field-1024x719.png\")
<\/a>Electric lines of forces<\/h3>\n\n\n\n
Electrostatic Potential<\/h2>\n\n\n\n
$V=\\frac{W}{q}$<\/li>
$V=\\frac{1}{4\\pi \\epsilon _{0}}\\frac{q}{r}$<\/li>Potential Difference<\/h3>\n\n\n\n
$A$ to $B$, $V_{B}-V_{A}=\\frac{W}{q}$
and do not consider to forget the signs of both $W$ and $q$.<\/li>
$V=\\int \\frac{1}{4\\pi \\epsilon _{0}}\\frac{dq}{r}$<\/li>
$dV=-E\\cdot dr$
or, $dV=-(E_{x}dx+E_{y}dy+E_{z}dz)$
components of E are related to corresponding derivatives of V in the following manner
$E_{x}=\\frac{dV}{dx}$
$E_{y}=\\frac{dV}{dy}$
$E_{z}=\\frac{dV}{dz}$<\/li><\/ol>\n\n\n\nEquipotential surfaces<\/h3>\n\n\n\n
Electric Potential Energy<\/h3>\n\n\n\n
![\"electric](\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2015\/08\/elecpot_eq71.png\")
<\/a><\/figure><\/div>\n\n\n\n
<\/p>\n\n\n\nElectric field intensity and potential due to different charge distribution<\/h2>\n\n\n\n
let $\\lambda$ be the charge per unit length of the wire
(a) Field intensity at a distance $r$ from the wire is $E=\\frac{\\lambda}{2\\pi\\epsilon_{0}r}$
(b) Electric potential due to infinite wire can not be found but the potential difference between two points is given as $V_B-V_A=-\\frac{\\lambda}{2\\pi\\epsilon_{0}}ln\\frac{r_{B}}{r_{A}}$<\/li>
$E=\\frac{qx}{4\\pi\\epsilon_{0}\\left ( x^{2} +r^{2}\\right )^{\\frac{3}{2}}}$
where $x$ is the distance of point $P$ from the center of the ring. Electric field is directed away from the ring if it is positively charged and towards it if it is negatively charged.
(b) Electric potential at this point $P$ would be
$V=\\frac{q}{4\\pi\\epsilon{0}\\sqrt{x^{2}+r^{2}}}$
(c) From above equations we can conclude that at the center electric field $E=0$ and $V=\\frac{q}{4\\pi\\epsilon_{0}r}$ which is maximum value for potential .Electric field intensity is maximum when $x=\\pm \\frac{r}{\\sqrt{2}}$ it is
$E_{max}=\\frac{1}{4\\pi \\epsilon _{0}}\\sqrt{\\frac{3}{2}}\\cdot \\frac{q}{r^{2}}$
also the field intensity and electric potential both are zero at infinity .<\/li>
If $\\lambda$ is the charge per unit length on the half ring of radius $r$ then electric field intensity at center of the ring would be
$E=\\frac{\\lambda}{2\\pi\\epsilon_{0}r}$
and electric potential at center of the half ring would be
$V=\\frac{\\lambda}{4\\epsilon_{0}}$<\/li>
If $q$ is the total amount of charge on a disk of radius $R$ then surface charge density of the disk would be$\\sigma=\\frac{q}{\\pi R^{2}}$let $r$ be the distance of the point $P$ on the axis from the center of the disk then electric field intensity at point $P$ would be$E=\\frac{\\sigma}{2\\epsilon_{0}}\\left [ 1-\\frac{r}{\\sqrt{r^{2}-R^{2}}} \\right ]$Its direction will be along the axis. For positively charged particles , it would be away from the disk and for negatively charged it is towards the disk.Now electric potential at point P will be$V=\\frac{\\sigma}{2\\epsilon_{0}}\\left [ \\sqrt{r^{2}-R^{2}} – r^{2} \\right ]$From above two equations we can conclude that\n\n
$E=\\frac{\\sigma}{2\\epsilon_{0}}$
$V=\\frac{\\sigma R}{2\\epsilon_{0}}$<\/li>\n<\/ul>\n<\/li><\/ol>\n\n\n\nElectric Dipole:<\/h2>\n\n\n\n
If $2a$ is the distance between two charges $+q$ and $-q$ then electric dipole moment is given as
$\\vec{p}=2q\\vec{a}$<\/p>\n\n\n\nElectric field due to dipole<\/h3>\n\n\n\n
$E_{axis}=\\frac{1}{4\\pi\\epsilon_{0}}\\frac{2p}{r^{3}}$
direction would be along the direction of dipole moment.
$V=\\frac{1}{4\\pi\\epsilon_{0}}\\frac{p}{r^{2}}$
On equatorial point<\/strong>
$E_{equitorial}=\\frac{1}{4\\pi\\epsilon_{0}}\\frac{p}{r^{3}}$
Direction would be opposite to the direction of dipole moment and potential would be zero.<\/p>\n\n\n\nTorque on a dipole in an external field<\/h3>\n\n\n\n
potential energy of a dipole in an electrostatic field
$U=-\\vec{p}\\cdot\\vec{E}$<\/p>\n\n\n\nGauss’s Law<\/h2>\n\n\n\n
Capacitance<\/h2>\n\n\n\n
Download links<\/h3>\n\n\n\n