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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.

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: $\stackrel{\to }{E}=\frac{2\stackrel{\to }{P}}{4\pi {\epsilon }_{\circ }{r}^{3}}$

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

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

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:  (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:  (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 'Q'

Electric Potential to a small Electric Dipole:

Electric Potential to Uniformly Charged Thin Shell:

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

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:

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:

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

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.

Resistance: Resistance 'R' of a wire is given by, $R=\rho \frac{L}{A}$ ( Where 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: $\stackrel{\to }{J}=\sigma \stackrel{\to }{E}$

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: ${\rho }_{\text{T}}={\rho }_{\text{o}}\left(1+\alpha \left(T-{T}_{\text{o}}\right)$

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:  (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 MagnetismChapter 5: Magnetism and MatterChapter 6: Electromagnetic Induction: Chapter 7: Alternating CurrentChapter 8: Electromagnetic Waves
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