What is Electrostatics?

Electrostatics is the study of electric charges at rest.

The study of stationary electric charges at rest is known as Electrostatics. An Electroscope is used to detect the charge on a body, with the Pith Ball Electroscope and Gold Leaf Electroscope being two types of electroscopes. The Gold Leaf Electroscope, invented by Bennet, not only detects a charge, but also the nature and quantity of the charge.

Conductors, Insulators, and Semiconductors

A body in which electric charge can easily flow through is called a conductor (e.g. metals).

A body in which electric charge cannot flow is called an insulator or dielectric (e.g. glass, wool, rubber, plastic, etc.).

Semiconductors are substances that lie between conductors and insulators, such as silicon and germanium.

Dielectric Strength: It is the minimum electric field intensity required to disrupt the insulating properties of an insulator.

The dielectric strength of air is $3\ast {10}^{6}V/m$

The Dielectric Strength of Teflon is $60\ast {10}^{6}V{m}^{-1}$

The maximum charge a sphere can hold is contingent upon the size and dielectric strength of the medium it is placed in.

1. The maximum charge density of a sphere of radius R in terms of electric intensity E at a distance r in free space is $E\epsilon ₀(R/r)²$.

2. When the electric field in the air surpasses its dielectric strength, air molecules become ionized, which are then accelerated by the fields, causing the air to become a conductor.

Surface Charge Density σ

The surface charge density σ of a conductor is defined as the charge per unit area, given by the equation $\sigma =\frac{q}{A}$, where q is the total charge and A is the area. When A is equal to 1 m², then σ = q.

The Surface Charge Density has a unit of coulomb/meter and its dimensions are ATL^-2. It is used in the formula for the charged disc, charged conductor and an infinite sheet of charge, etc. Its value depends on the shape of the conductor and the presence of other conductors and insulators in the vicinity of the conductor.

1. \begin{array}{l}\sigma\alpha \frac{1}{r^{2}};\text{i.e.}\frac{\sigma_1}{\sigma_2} = \frac{r_{2}^{2}}{r_{1}^{2}}\end{array}

2. σ is maximum at pointed surfaces and minimum for plane surfaces.

Surface Charge Density is greatest at the corners of rectangular laminas and at the vertex of the conical conductor.

Electric Flux

The number of electric lines of force crossing a surface normal to the area gives electric flux ΦE.

Electric flux through an elementary area ds is defined as the scalar product of area dA and field E.

$d\Phi E=Eds\ast cos\theta$

\begin{array}{l} \phi_E = \int \vec{E} \cdot d\vec{s} \end{array}

The electric flux will be at its greatest when the electric field is perpendicular to the surface area $(\Phi =E\ast d\ast s)$

Electric Flux will be minimum when the field is parallel to the area $(d\Phi =0)$

For a closed surface, outward flux is negative and inward flux is positive

Electric Potential (V)

The electric potential at a point in a field is the amount of work done in bringing a unit positive charge from infinity to the point. It is equal to the electric potential energy of a unit positive charge at that point.

It is a scalar

The S.I. unit for voltage is the volt.

Electric Potential at a distance ’d’ due to a point charge q in air or vacuum is $$V = \frac{1}{4\pi \varepsilon_0}.\frac{q}{d}$$

Electric Potential (V): $$-\int{\vec{E}.\vec{d}x}$$

\begin{array}{l}v = -E \cdot x\end{array}

Work done in moving a charge q through a potential difference V is W = qV joules, where a positive charge moves from high potential to low potential and an electron moves from low potential to high potential when left free.

Gain in Kinetic Energy: $\frac{1}{2}m{v}^2=qV$

Gain in the Velocity:

$\begin{array}{l}v=\sqrt{\frac{2qV}{m}}\end{array}$

Equipotential Surface

A surface on which all points are at the same potential.

1. The equipotential surface is perpendicular to the electric field.

2. Work done in moving a charge on an equipotential surface is zero.

In the Case of a Hollow Charged Sphere

1. The intensity of the electric field at any point inside the sphere is zero.

2. The intensity at any point on the surface is the same and is given by $$\frac{1}{4\pi \varepsilon_0}.\frac{q}{r^2}$$

3. Outside the sphere $$\frac{1}{4\pi \varepsilon_0}.\frac{q}{d^2}$$, where d is the distance from the centre, it behaves as if the whole charge is at its centre.

Electric field Intensity in vector form $$\vec{E}=\frac{1}{4\pi \varepsilon_0}.\frac{q}{d^3}\vec{d} ;\text{or}; \vec{E}=\frac{1}{4\pi \varepsilon_0}.\frac{q}{d^3}\hat{d}$$

The electric field intensity resulting from multiple sources follows the principle of superposition.

$\begin{array}{l}\overrightarrow{E}={\overrightarrow{E}}_1+{\overrightarrow{E}}_2+{\overrightarrow{E}}_3+\dots \end{array}$

In the Case of a Solid Charged Sphere

The potential at any point inside the sphere is equal to the potential at any point on its surface.

\begin{array}{l}V = \frac{q}{4\pi \varepsilon_0 r}\end{array}

It is an equipotential surface. Outside the sphere, the potential decreases as the distance of the point from the centre increases.

\begin{array}{l}V = \frac{q}{4\pi {{\varepsilon }_{0}}d}\end{array}

Note: Within a non-conductive, charged sphere, an electric field is present.

Electric Intensity Within the Sphere

\begin{array}{l}E = \frac{1}{4\pi\varepsilon_0}\cdot\frac{Q}{R^3}\cdot d\end{array}

Inside the sphere, the electric field ∝ d; outside the sphere, the electric field falls off like 1/d².

Electron Volt

The unit of energy in particle physics is referred to as an electronvolt (eV).

1 eV = 1.602 x 10^-19 J.

Charged Particle in an Electric Field

When a positive test charge is fired in the direction of an electric field

• It accelerates
• Its kinetic energy increases
• Its potential energy decreases.

A charged particle of mass (m), carrying a charge (q), and falling through a potential (V) acquires a speed of $\sqrt{\frac{2Vq}{m}}$.

Electric Dipole

A pair of equal and opposite charges separated by a constant distance is referred to as an electric dipole.

$\overrightarrow{P}=q\cdot 2\overrightarrow{l}$

Dipole Moment

It is the product of one of the charges and the distance between the charges. It is a vector directed from the negative charge towards the positive charge along the line joining the two charges.

The torque acting on an electric dipole placed in a uniform electric field is given by the relation

$(\overrightarrow{\tau }=\overrightarrow{P}\times \overrightarrow{E}i.e.,\tau =PE\sin \theta ),\mathrm{where}(\theta )\mathrm{is\; the\; angle\; between}(\overrightarrow{P})\mathrm{and}(\overrightarrow{E})$

The electric intensity (E) on the axial line at a distance d from the center of an electric dipole is $$E=\frac{1}{4\pi {{\varepsilon }_{0}}}\cdot \frac{2Pd}{{{({{d}^{2}}-{{l}^{2}})}^{2}}}$$ and on equatorial line, the electric intensity (E) $$=\frac{1}{4\pi {{\varepsilon }_{0}}}\cdot \frac{P}{{{({{d}^{2}}+{{l}^{2}})}^{3/2}}}$$.

⇒ For a short dipole, i.e., if $l\ll d$, then the electric intensity on the equatorial line is given by $\frac{1}{4\pi {\epsilon }_0}\cdot \frac{P}{d^3}$.

The potential due to an electric dipole on the axial line is $$V = \frac{1}{4\pi \varepsilon_0}\cdot \frac{P}{(d^2-l^2)}$$ and at any point on the equatorial line it is zero.

• When two equal charges of opposite polarity, +Q and -Q, are separated by a * distance
• The electric potential on the perpendicular bisector of the line joining the * charges is equal to zero.
• The bisector is an equipotential and has a potential of zero.
• The work done in moving a charge along this line is zero.
• The electric intensity at any point on the bisector is perpendicular to the bisector.
• The electric intensity at any point on the bisector parallel to the bisector is equal to zero.

Combination of Electric Fields Due to Two Point Charges

Similar Charges Resulting in Consequences

If charges q₁ and q₂ are separated by a distance r, a null point (where the resulting field intensity is zero) is formed on the line joining those two charges.

1. A point of no charge is formed within the charges.

2. Weak charge is located nearer to the null point.

![Combined field due to 2 point charges]()

If x is the distance of the null point from q1,

$\frac{{\text{q}}_{\text{1}}}{{\text{x}}^{\text{2}}}=\frac{q_2}{{(r-x)}^2}$

**$(x=\frac{r}{\sqrt{\frac{q_2}{q_1}}}+1)\ast \ast ,where(q_1)and(q_2)$ are like charges.

Two Dissimilar Charges Resulting in a Difference

• 1. If q₁ and q₂ are unlike charges, then a null point is formed on the line connecting the two charges.
• 2. A null point is formed outside the charges.
• 3. Null point is from a weaker charge.
• 4. $\begin{array}{l}\frac{{\text{q}}_{\text{1}}}{{\text{x}}^{\text{2}}}=\frac{q_2}{{(r+x)}^2}\end{array}$

In the above formulae $\frac{q_2}{q_1}$ is the numerical ratio of charges.

Zero Potential Point Due to Two Charges

If two unlike charges q₁ and q₂ are separated by a distance r, the net potential is zero at two points on the line joining them.

One between them and the other outside the charges.

Both points are closer to a weak charge (q₁).

$\begin{array}{l}\frac{{\text{q}}_{\text{1}}}{{\text{x}}^{}}=\frac{q_2}{(r-x)}\end{array}$ (for point 1, within the charges)

$$(\frac{{q_{1}}}{{y^{}}}=\frac{{q_{2}}}{(r+y)},) where (q_{2}) $$ is the numerical value of the strong charge (for point 2, outside the charges).

$\begin{array}{l}\Rightarrow x=\frac{r}{\frac{q_2}{q_1}+1};y=\frac{r}{\frac{q_2}{q_1}-1}\end{array}$

No potential point is formed due to the two similar charges.

Electric Lines of Force

The line of force is the path along which a unit +ve charge accelerates in the electric field. The tangent at any point to the line of force gives the direction of the field at that point.

Properties of Electric Lines of Force

• Two lines of force never cross.
• The number of lines of force passing normally through a unit area around a * point is equal in numerical value to E, the strength of the field at the point.
• Lines of force always originate or terminate on a charged conductor.
• Electric lines of force cannot form closed loops.
• Lines of force have a tendency to contract longitudinally and exert a force * of repulsion on one another laterally.
• If there is no electric field in a region of space, there will be no lines of force. Inside a conductor, there cannot be any lines of force.

The number of lines of force passing normally through a unit area around a point is numerically equal to E.

Lines of force in a uniform field are parallel to one another.

The Difference Between Electric and Magnetic Lines of Force

Electric lines of force never form closed loops, whereas magnetic lines of force always form closed loops.

Electric lines of force do not exist inside a conductor, however magnetic lines of force may exist inside a magnetic material.

Frequently Asked Questions on Electrostatics

Question: Is the electrostatic force between the two-point charges a central force?

Yes, the electrostatic force between two-point charges is a central force.

Yes, the electrostatic force between two point charges always acts along the line joining the two charges, making it a central force.

At what separation is the electrostatic force between two given charges maximum?

The electrostatic force between two given charges separated by a certain distance is greatest when the charges are in air or vacuum.

Does electrostatic force obey Newton’s third law?

Yes, electrostatic force obeys Newton’s third law.

Yes. If charge q₁ exerts a force on q₂, then q₂ exerts an equal and opposite force on q₁.

How Does Charging by Conduction Work?

Charging by conduction is a method in which a conductor is charged by bringing a body with an existing charge into contact with the conductor.