**Chapter 1: Electric Charges and Fields**

Electric Charge:The fundamental property of a particle due to which it feels a force when placed in a uniform magnetic or electric field is known as a charge.

Electric Charge:

**Conductors and Insulators:**The substances which allow electricity to pass through them easily are conductors whereas the substances which don't allow electricity to pass through them easily are called insulators.

**Charging by Induction:**When an electrified rod is brought near an uncharged conductor, due to the force of charges present on the rod the free electrons in a conductor rearrange themselves, this process is called charging by Induction.

**Coulomb’s Law:**Coulomb's law gives us the magnitude of the force between two point charges separated by a certain distance, i.e.$F=\frac{1}{4\pi {\epsilon}_{\circ}}\frac{\left|{Q}_{1}{Q}_{2}\right|}{{r}^{2}}$

**Electric Field Intensity:**The electric field intensity at a point due to a source charge is defined as the force experienced per unit positive test charge placed at that point without disturbing the source charge.

**Electric Field Intensity Due to a Point Charge: $E=\frac{1}{4\pi {\epsilon}_{\circ}}\frac{q}{{r}^{2}}$**

**Electric Field Lines:**Electric field lines are defined as the path along which a free unit positive charge would move.

**Electric Flux:**The total number of electric field lines crossing through a surface placed in an Electric field in a direction normal to the surface.

**Electric Dipole Moment:**Electric dipole moment for a pair of opposite charges with magnitude '

*q*' can be defined as the product of either of the charges and the length of the electric dipole.

**Electric Field on Axial Line of a small Electric Dipole: $\overrightarrow{E}=\frac{2\overrightarrow{P}}{4\pi {\epsilon}_{\circ}{r}^{3}}$**

Electric Field on the Equatorial Plane of a small Electric Dipole: $\overrightarrow{E}=\frac{-\overrightarrow{P}}{4\pi {\epsilon}_{\circ}{r}^{3}}$

Electric Field on the Equatorial Plane of a small Electric Dipole: $\overrightarrow{E}=\frac{-\overrightarrow{P}}{4\pi {\epsilon}_{\circ}{r}^{3}}$

**Dipole in a Uniform External Field:**Dipole is placed inside a uniform electric field feels a torque, which is given by, $\overrightarrow{\tau}=\overrightarrow{p}\times \overrightarrow{E}$

**Gauss's Law:**It states that the total electric flux through a closed surface enclosing a charge is equal to $\frac{1}{{\epsilon}_{\text{o}}}$ times the magnitude of the charge enclosed.

**Gaussian Surface:**Any surface that we choose to enclose the charge is known as Gaussian Surface.

**Gauss's Theorem:**

**Field due to an Infinitely Long Straight Uniformly Charged Wire:**$E=\frac{\lambda}{2\pi {\epsilon}_{\text{o}}r}$ (Where '$\lambda $' is linear charge density of the wire)

**Field due to an Infinitely Charged Plane Sheet: $E=\frac{\sigma}{2{\epsilon}_{\text{o}}}$**(Where $\text{'}\sigma \text{'}$ is the surface charge density of the sheet)

**Field due to a Uniformly Charged Thin Shell:**${E}_{\text{outside}}=0,{E}_{\text{inside}}=\frac{q}{4\pi {\epsilon}_{\text{o}}{r}^{2}}$ (Where

*'q'*is the charge on the surface of the shell)

**Chapter 2: Electrostatic Potential and Capacitance**

**Electric Potential:**Electric potential at any point is defined as the amount of work done in bringing a unit positive charge from infinity to that point.

**Electric Potential Due to a Point Charge '**

Electric Potential to a small Electric Dipole: $E=\frac{\overrightarrow{p}.\hat{r}}{4\pi {\epsilon}_{\text{o}}{r}^{2}}$

Electric Potential to Uniformly Charged Thin Shell: ${V}_{\text{outside}}=\frac{q}{4\pi {\epsilon}_{\text{o}}r}(r\ge R),{V}_{\text{inside}}=\frac{q}{4\pi {\epsilon}_{\text{o}}R}(r\le R)$

Electrostatic potentialis constant throughout the volume of the conductor and has the same value (as inside) on its surface

*Q'*: $V\left(r\right)=\frac{Q}{4\pi {\epsilon}_{\text{o}}r}$Electric Potential to a small Electric Dipole: $E=\frac{\overrightarrow{p}.\hat{r}}{4\pi {\epsilon}_{\text{o}}{r}^{2}}$

Electric Potential to Uniformly Charged Thin Shell: ${V}_{\text{outside}}=\frac{q}{4\pi {\epsilon}_{\text{o}}r}(r\ge R),{V}_{\text{inside}}=\frac{q}{4\pi {\epsilon}_{\text{o}}R}(r\le R)$

Electrostatic potential

**Equipotential Surface: **Any surface where each and every point has the same electric potential is known as an equipotential surface.

**Relation between Field and Potential: $E=-\frac{dV}{dr}$
Electric Potential Energy: **Electric potential energy of a charge is defined as the amount of work done in bringing a charge from infinity to that point.

**Electric Potential Energy of a System of two Charges: $U\left(r\right)=\frac{{q}_{1}{q}_{2}}{4\pi {\epsilon}_{\text{o}}r}$**

**Electric Potential Energy of a Charge in an External Field:**The Electric potential energy of a charge

*'q'*at a distance

*'r'*in an external field =

*q V(r)*(where

*V(r)*is the external potential at

*'r'*)

**Electric Potential Energy of a System of two Charges in an External Field: $U\left(r\right)={q}_{1}V\left({r}_{1}\right)+{q}_{2}V\left({r}_{2}\right)+\frac{{q}_{1}{q}_{2}}{4\pi {\epsilon}_{\text{o}}{r}_{12}}$**

**Electric Potential Energy of a Dipole in an External Field: $U\left(\theta \right)=-\overrightarrow{p}.\overrightarrow{E}$**

**Electrostatic shielding: **Inside a conductor, electrostatic field is zero. Whatever be the charge and field configuration outside, any cavity in a conductor remains shielded from the outside electric influence, this is known as Electrostatic shielding.

**Electric field at the surface of a charged conductor: $E=\frac{\sigma}{{\epsilon}_{\text{o}}}$**

**Non-polar dielectrics: **The centre of positive charge coincides with the centre of negative charge in the molecule.

**Polar dielectrics: **The centers of positive and negative charges do not coincide because of the asymmetric shape of the molecules.

**Polarisation: **A dielectric develops a net dipole moment in the presence of an external field. The dipole moment per unit volume is called polarisation.

**Capacitance: **The ability of a conductor to hold the charge is known as capacitance.

**Capacitance of a Parallel Plate Capacitor: **$C=\frac{Q}{V}=\frac{{\epsilon}_{\text{o}}A}{d}$ (Where *'A'* is the area of the plates and *'d'* is the separation between the plates)

**Effect of Dielectric on Capacitance: **$C=\frac{K{\epsilon}_{\text{o}}A}{d}$(Where *'K'* is the dielectric constant of the medium)

**Net Capacitance in Series Combination: $\frac{1}{{C}_{\text{series}}}=\frac{1}{{C}_{1}}+\frac{1}{{C}_{2}}+.....+\frac{1}{{C}_{\text{n}}}$
Net Capacitance in Parallel Combination: ${C}_{\text{parallel}}={C}_{1}+{C}_{2}+{C}_{3}+....+{C}_{\text{n}}$**

**Energy Stored in a Capacitor: $u=\frac{1}{2}\frac{{Q}^{2}}{C}=\frac{1}{2}{\epsilon}_{\text{o}}{E}^{2}$ **(Where '*u'* is the energy density or Energy stored per unit volume of the space.)

**Chapter 3: Current Electricity**

**Electric Current:**Flow of electric charge per unit time is simply known as Electric Current.

**Ohm's Law: **Electric current flowing through a conductor is directly proportional to the potential difference across the two ends of the conductor; given that physical quantities such as temperature, mechanical strain, etc. are constant. i.e. $I=\left(\frac{1}{R}\right)VorV=\left(R\right)I$

**Resistance: **Resistance *'R'* of a wire is given by, $R=\rho \frac{L}{A}$ ( Where $\text{'}\rho \text{'}$is the resistivity of the wire)

**Resistivity: ** Resistance per unit length per unit area of an electrical wire is known it's resistivity.

**Conductivity: $\sigma =\frac{1}{\rho}$
Relation between Current Density and Electric Field: $\overrightarrow{J}=\sigma \overrightarrow{E}$**

**Drift Velocity:**The average velocity attained by some particle such as an electron due to the influence of an electric field is termed as the drift velocity.

**Mobility:**Magnitude of drift velocity per unit electric field is known as mobility.

**Temperature dependence of Resistivity: ${\rho}_{\text{T}}={\rho}_{\text{o}}(1+\alpha (T-{T}_{\text{o}})$**

**Power:**Energy dissipated per unit time is known as Power. $P={I}^{2}R=\frac{{V}^{2}}{R}$

**Net resistance in Series Combination:**${R}_{\text{series}}={R}_{1}+{R}_{2}+{R}_{3}+.....+{R}_{\text{n}}$

**Net Resistance in Parallel Combination:**$\frac{1}{{R}_{\text{parallel}}}=\frac{1}{{R}_{1}}+\frac{1}{{R}_{2}}+\frac{1}{{R}_{3}}+.....+\frac{1}{{R}_{\text{n}}}$

**Voltage Drop across a Battery:**$V=\epsilon -Ir$ (Where

*'r'*is the internal resistance of the battery and

*'E'*is the emf of the battery)

**Kirchhoff's Junction Rule:**At any junction, the sum of the currents entering the junction is equal to the sum of currents leaving the junction.

**Kirchoff's Loop Role:**The algebraic sum of changes in potential around any closed loop involving resistors and cells in the loop is zero

**Chapter 4: Moving Charges and Magnetism**

**Chapter 5: Magnetism and Matter**

**Chapter 6: Electromagnetic Induction:**

**Chapter 7: Alternating Current**

**Chapter 8: Electromagnetic Waves**