Electrostatics

×

Arial Calibri Cambria Comic Courier Seoge Times

Electrostatics is the branch of physics that studies the charges at rest.

×

---

Electric Charge -

---

Charge is that intrinsic property that is associated with the matter due to which it produces and experiences electrical and magnetic effects.

Type of charges
1. Positive charge - Loss of electron (Size increased)
2. Negative charge - Gain of electron ( Size decreased)

✍ Like charges repel each other while unlike charges attract each other.

S.I. unit of charge is coulomb (C), $\left(1\text{mC}={10}^{-3}\text{C},1\mu \text{C}={10}^{-6}\text{C},\mathrm{1n}\text{C}={10}^{-9}\text{C}\right)$

C.G.S. the unit of charge is e.s.u. $1\text{C}=3\times {10}^9$

The Dimensional formula is given by $=[\text{A T}]$

×

---

Properties of Charge

---

Charges can be added or subtracted algebraically.

Law of conservation of charge - Charge can neither be created nor be destroyed.

The numerical value of an elementary charge is independent of velocity.

Charge cannot exist without mass though mass can exist without charge.

When a charged body is put in contact with an uncharged body, the uncharged body becomes charged due to transfer of electrons from the charged body to the uncharged body.

Rest - Electric field
Uniform Motion - Electric field & Magnetic field
Nonuniform Motion - Electric field, Magnetic field & EMW

Charge resides on the outer surface of a conductor because like charges repel and try to get as far away as possible from one another and stay at the farthest distance from each other which is the outer surface of the conductor.
A solid & hollow conducting sphere of the same outer radius will hold a maximum equal charge.
A soap bubble expands on charging.

When a physical quantity can have only discrete values rather than any value, the quantity is said to be quantised. The smallest charge that can exist in nature is the charge of an electron. If the charge of an electron $\left(-1.6\times {10}^{-19}\text{C}\right)$ is taken as elementary unit i.e. quanta of charge the charge on anybody will be some integral multiple of e i.e., with , Charge on a body can never be or etc.

Q = n × e

n = Q ÷ e

×

---

Methods of Charging

---

In friction when two bodies are rubbed together, electrons are transferred from one to another. As a result of this one body becomes positively charged while the other is negatively charged.

1. Clouds become charged by friction.
2. Ebonite on rubbing with wool becomes negatively charged making the wool positively charged.
3. A glass rod is rubbed with silk, the glass rod becomes positively while silk becomes negatively
4. A plastic rod is rubbed with furr, the plastic rod becomes negatively while furr becomes positively.

Note : Insulator can be charging using friction. Qus - Insulators can be charged by which of the following process? (COMEDK 2021)

1. Induction
2. Diverging
3. Friction
4. Heating

charging by friction is based on conservation of charge, both positive and negative charges in equal amounts appear simultaneously due to the transfer of electrons from one body to another.

If a charged body is brought near an uncharged body, the charged body will attract the opposite charge and repel a similar charge present in the uncharged body. As a result of this one side of the neutral body (closer to charged body) becomes oppositely charged while the other is similarly charged. This process is called induction.
Note: Inducting body (inducer) neither gains nor loses charge.

Take two conductors, one charged and the other uncharged. Bring the conductors in contact with each other. The charge (whether negative or positive) under its own repulsion will spread over both the conductors. Thus, the conductors will be charged with the same sign. This is called as charging by conduction (through contact).
Note: A truck carrying explosives has a metal chain touching the ground, to conduct away the charge produced by friction.

×

---

Coulomb's Law

---

If two stationary & point charges $Q_1$ and $Q_2$ are kept at a distance r, Then Electrostatic force of attraction or repulsion b/w two static point charges is -

1. directly proportional to product of charges.
2. inversely proportional to square of distance b/w charges.

$\text{F}=\text{k}{\displaystyle \frac{{\text{q}}_1{\text{q}}_2}{{\text{r}}^2}}={\displaystyle \frac{1}{4\pi {\epsilon }_0}{\displaystyle \frac{{\text{q}}_1{\text{q}}_2}{{\text{r}}^2}}}$ ${}_{\mathrm{}}=$ $\left[M^1{L}^1{T}^{-2}\right]$

where k is a proportionality constant. $k={\displaystyle \frac{1}{4\pi {\epsilon }_0}}=9\times {10}^9{\displaystyle \frac{\text{N}{\text{m}}^2}{{\text{C}}^2}}$ ${}_{\mathrm{}}=$ $\left[M^1{L}^3{T}^{-4}{A}^{-2}\right]$

Where ${\epsilon }_0=$ Absolute permittivity of air or free space $=8.85\times {10}^{-12}{\displaystyle \frac{C^2}{N{m}^2}}\left(={\displaystyle \frac{\text{ Farad }}{m}}\right)$ ${}_{\mathrm{}}=$ $\left[M^{-1}{L}^{-3}{T}^4{A}^2\right]$

1. Electrostatic force is central force.
2. Electrostatic force is conservative in nature.
3. Electrostatic force is follows inverse square law.
4. Like charges repel and unlike charges attract each other.
5. Coulomb's Force is Vector Quantity - direction always along the line of adjoining.

×

---

When a dielectric medium is completely filled in b/w charges rearrangement of the charges inside the dielectric medium takes place and the force between the same two charges decreases by a factor of dielectric constant.

×

---

Let there be two point charges $Q_1$ and $Q_2$, such that $\overrightarrow{r_1}$ and $\overrightarrow{r_2}$ represent the position of two vectors, respectively. the two charges will exert force on each other,

let $\overrightarrow{F_{12}}$ be the force exerted by the charge $Q_2$ on $Q_1$
suppose the corresponding position vector from $Q_2$ to $Q_1$ given by $\overrightarrow{r_{12}}.$ thus, using triangle law, $\overrightarrow{r_{12}}=\overrightarrow{r_1}–\overrightarrow{r_2}$
The direction of position vector from $\overrightarrow{r_2}$ to $\overrightarrow{r_1}$ is given by $\widehat{r_{12}}=\frac{\overrightarrow{r_{12}}}{\left|\overrightarrow{r_{12}}\right|}$ Therfore, the force acting on the charge $Q_1$ due to $Q_2$ in vector form can be given as $\begin{array}{c}{\overrightarrow{F}}_{12}=\frac{1}{4\pi {\in }_0}\frac{q_1{q}_2}{r_{12}^2}{\hat{r}}_{12}=\frac{1}{4\pi {\in }_0}\frac{q_1{q}_2}{r_{12}^3}{\overrightarrow{r_{12}}}_{}\end{array}$

Let $\overrightarrow{F_{21}}$ be the force exerted by the charge $Q_2$ on $Q_2$
suppose the corresponding position vector from $Q_1$ to $Q_2$ given by $\overrightarrow{r_{21}}.$ thus, using triangle law, $\overrightarrow{r_{21}}=\overrightarrow{r_2}–\overrightarrow{r_1}$
The direction of position vector from $\overrightarrow{r_1}$ to $\overrightarrow{r_2}$ is given by $\widehat{r_{21}}=\frac{\overrightarrow{r_{21}}}{\left|\overrightarrow{r_{21}}\right|}$ Therfore, the force acting on the charge $Q_1$ due to $Q_1$ in vector form can be given as $\begin{array}{c}{\overrightarrow{F}}_{21}=\frac{1}{4\pi {\in }_0}\frac{q_1{q}_2}{r_{21}^2}{\hat{r}}_{21}=\frac{1}{4\pi {\in }_0}\frac{q_1{q}_2}{r_{21}^3}{\overrightarrow{r_{21}}}_{}\end{array}$

From above result, we conclude that force on second charge exerted by first charge is equal and oposite to that force on first charge exerted by second charge. thus $\overrightarrow{F_{21}}=–\overrightarrow{F_{12}}$ , coulombs law upholds newtons third law of motion, stating that every action has an equal and oposite reaction.

×

---

×

---

The region around an electric charge where its influence can be observed.
The electric field $\overrightarrow{E}$ \overrightarrow{E}=\frac{\overrightarrow{F}}{q}=\frac{1}{4\pi {ϵ}_0}\frac{Q_{}}{r^2}\widehat{r_{}}=\frac{{\mathrm{K\; Q}}_{}}{r^2}\widehat{r_{}}$$ is a vector quantity.

The SI unit of an electric field is volt/meter.
For a circular ring of Radius R with uniformly distributed charge ${\displaystyle \overrightarrow{E}=\frac{KQx}{(x^2+R^2{)}^{3/2}}\hat{x}}$

×

---

• The tangent of electric field represents the direction of net electric field or force at the point.
• In a charge-free region, Field lines show a continuous curve w/o having any break. (conservation of charge)
• Two electric field lines never (intersect) cross each other on electric fields. because the electric field can never have two directions at a particular point.
• For dipole - These electric field lines always begin on the positive charge and end in the negative charge.
• For isolated positive- the field lines start from positive or end at infinity.
• For isolated negative- the field lines start from infinity or end at negative.
• Electric field lines formes open loop. but magnetic field lines forms close loop.
• The electric field lines are perpendicular to the surface of the charge.
• Numbers of electric field lines are proportional to the magnitude of charge.
• Electric potential is decreased in the direction of electric field lines.
• Electric field lines never go through a conductor. As inside a conductor, the electric field is always zero.
• E.F.L. can be affected by the attractive force b/w two charges. Due to this, they tend to contract in length.
• E.F.L. can be affected by the repulsive force b/w two like charges. Due to this, they tend to diverge in length.
• The field lines are uniformly spaced, parallel, and straight in a uniform electric field.

×

---

$\mathrm{dipole\; moment}=\mathrm{charge}\times \mathrm{small\; displacement}$

×

---

Linear Charge Distribution $\lambda ={\displaystyle \frac{Q}{L}}$ ${\displaystyle \frac{C}{m^{}}}$

Surface charge distribution $\sigma ={\displaystyle \frac{Q}{A}}$ ${\displaystyle \frac{C}{m^2}}$

Volume Charge Distribution $\rho ={\displaystyle \frac{Q}{V}}$ ${\displaystyle \frac{C}{m^3}}$

×

---

The total no. of electric field lines passing through an particular area in a unit time is known as electric flux.

Electric flux is the flow rate of an electric field through an area. It is proportional to the number of electric field lines passing through a virtual surface.
$\begin{array}{c}{\mathrm{\Phi <!--\; \Phi \; -->}}_E=\stackrel{\to <!--\; \to \; -->}{E}\cdot <!--\; \cdot \; -->\stackrel{\to <!--\; \to \; -->}{A}=EA\cos <!--\; \; -->\mathrm{\theta <!--\; \theta \; -->}\end{array}$ The SI unit of electric flux is volt x meter.

×

---

The total outgoing flux linked with a closed surface is times the charge enclosed by the closed surface. $\begin{array}{c}\oint \overrightarrow{E}.\overrightarrow{\mathrm{dA}}=\frac{\mathrm{Q}}{{\in }_0}\end{array}$
Gaussian Surface -
Electric field due to Uniformly charged Straight wire
Electric field because of Uniformly charged Infinite plate sheet:
Electric Field because of a uniformly charged thin spherical shell:

×

---

$E_{center}{=}_{}{0}_{}$

$E_{inside}{=}_{}{\displaystyle \frac{\mathrm{K\; Q\; r}}{R^3}}$

$E_{surface}{=}_{}{\displaystyle \frac{\mathrm{K\; Q}}{R^2}}$

$E_{outside}{=}_{}{\displaystyle \frac{\mathrm{K\; Q}}{r^2}}$

×

---

Centre	Inside	Surface	Outside
r = 0	r R	r = R	r R
$E_{center}{=}_{}{0}_{}$	$E_{inside}{=}_{}{0}_{}$	$E_{surface}{=}_{}{\displaystyle \frac{\mathrm{K\; Q}}{R^2}}$	$E_{outside}{=}_{}{\displaystyle \frac{\mathrm{K\; Q}}{r^2}}$

×

---

×

---

×

---

$\tau =\overrightarrow{p}\times \overrightarrow{E}$

---