Physical World and Measurement
Motion in a straight line
Motion in a Plane
Force and Laws Of Motion
Work, Energy and Power
System of Particles and Rotational Motion
- Notes and Study Materials -System of Particles and Rotational Motion
- Online Test Series 1 -NEET & AIIMS Past Years based -System of Particles and Rotational Motion
- Online Test Series 2-NCERT Based – System of Particles and Rotational Motion
- Online Test Series 3: Daily Practice Papers – System of Particles and Rotational Motion
Mechanical Properties of Solids
Mechanical Properties of Fluids
Thermal Properties of Matter
Kinetic Theory of Gases
Electric Charges and Fields
Electrostatic Potential and Capacitance
- Notes and Study Materials -Electrostatic Potential and Capacitance
- Online Test Series 1 -NEET & AIIMS Past Years based -Electrostatic Potential and Capacitance
- Online Test Series 2-NCERT Based – Electrostatic Potential and Capacitance
- Online Test Series 3: Daily Practice Papers – Electrostatic Potential and Capacitance
Moving Charges and Magnetism
Magnetism and Matter
Ray Optics and Optical Instruments
- Notes and Study Materials -Ray Optics and Optical Instruments
- Online Test Series 1 -NEET & AIIMS Past Years based -Ray Optics and Optical Instruments
- Online Test Series 2-NCERT Based – Ray Optics and Optical Instruments
- Online Test Series 3: Daily Practice Papers – Ray Optics and Optical Instruments
Dual Nature of Radiation and Matter
- Notes and Study Materials -Dual Nature of Radiation and Matter
- Online Test Series 1 -NEET & AIIMS Past Years based -Dual Nature of Radiation and Matter
- Online Test Series 2-NCERT Based – Dual Nature of Radiation and Matter
- Online Test Series 3: Daily Practice Papers – Dual Nature of Radiation and Matter
Semiconductor Electronics : Materials, Devices & Simple Circuits
- Notes and Study Materials -Semiconductor Electronics : Materials, Devices & Simple Circuits
- Online Test Series 1 -NEET & AIIMS Past Years based -Semiconductor Electronics : Materials, Devices & Simple Circuits
- Online Test Series 2-NCERT Based – Semiconductor Electronics : Materials, Devices & Simple Circuits
- Online Test Series 3: Daily Practice Papers -Semiconductor Electronics : Materials, Devices & Simple Circuits
Experimental Skills in Physics
Notes and Study Materials -Electrostatic Potential and Capacitance
About this unit
Electric charges and their conservation. Coulomb’s law-force between two point charges, forces between multiple charges; superposition principle and continuous charge distribution. Electric field, electric field due to a point charge, electric field lines; electric dipole, electric field due to a dipole; torque on a dipole in a uniform electric field.Electric flux, statement of Gauss’s theorem and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside and outside) Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges: equipotential surfaces, electrical potential energy of a system of two point charges and of electric diploes in an electrostatic field. Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics and electric polarization, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor, Van de Graaff generator.
ELECTROSTATIC POTENTIAL AND CAPACITANCE
POTENTIAL DUE TO A POINT CHARGE
POTENTIAL DUE TO CONTINUOUS CHARGE DISTRIBUTION
POTENTIAL DUE TO A SYSTEM OF CHARGES
V = V1 + V2 + … + Vn
RELATION BETWEEN ELECTRIC FIELD AND POTENTIAL
CONSERVATIVE NATURE OF ELECTRIC FIELD
POTENTIAL ENERGY OF A SYSTEM OF CHARGES
- For an assembly of n charges
[Total number of intersection ] the potential energy is
- For a system of two charges.
- The energy required to take away the charges of a dipole at infinite distance
- The work done when a charge q is moved across a potential difference of V volt is given by W = qV
- When one electronic charge (1.6×10–19 coulomb i.e., charge of electron) is moved across one volt the work done is called one electron volt (eV). Thus 1eV = (1 volt) × (1.6×10–19 coulomb) = 1.6×10–19 joule.
POTENTIAL DUE TO VARIOUS CHARGE DISTRIBUTION
- Electric potential due to isolated point charge
- A circular ring of radius R with uniformly distributed charge Q
- A circular disc of radius R with uniformly distributed charge with surface charge density σ
- A finite length of charge with linear charge density
- Due to a spherical shell of uniformly distributed charge with surface charge density σ
- Due to a solid sphere of uniformly distributed charge with volume charge density ρ.
POTENTIAL DUE TO ELECTRIC DIPOLE
- Along axial line :
- Along equatorial line : Veq = zero
- At any point from the dipole :
- Electric field inside a charged conductor is zero
- Electronic lines of force are always perpendicular to the equipotential surfaces.
- The work done in moving a charge from a point to the other on an equipotential surface is zero as the potential difference between the two points is zero.
- The electric potential at a point due to a point charge decreases (or increases) by K-times if the distance between the charge and the point increases (or decreases) by K-times.
- A ring with a charge distribution behaves as a point charge for the points very far from its centre.
- The electric potential is constant inside a hollow charged sphere and it is also equal to its value on the surface but it varies inversely with the distance outside the sphere.
- The electric potential at points inside a solid sphere has a non-zero value and decreases as we go from the centre outwards. It behaves as a point charge for the points outside the sphere.
- The electric potential at a point due to a dipole varies directly with the dipole moment.
ELECTROSTATICS OF CONDUCTORS
- Inside a conductor, electric field is zero.
- The interior of a conductor can have no excess charge in static situation.
- Electric field at the surface of a charged conductor is
- Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point.
- Electrostatic potential is constant throughout the volume of the conductor and has the same value as on its surface.
- Surface density of charge is different at different points.
CAPACITORS AND CAPACITANCE
ENERGY STORED IN A CAPACITOR
SHARING OF CHARGES
PARALLEL PLATE CAPACITOR
EFFECT OF DIELECTRIC ON CAPACITANCE
- The unit farad is quite a big unit for practical purposes. Even the capacitance of a huge body like earth is 711 μF.
- A capacitor is a device which stores charges and produces electricity whenever required.
- If the two plates of a capacitor is connected with a conducting wire, sparking takes place which shows that electrical energy is converted into heat and light energy.
- A capacitor allows A.C. but doesn’t allow D.C. to pass through it.
- The capacitance of a capacitor increases with insertion of a dielectric between its plates and decreases with increase in the separation between the plates.
- The capacitance of a capacitor increases K times if a medium of dielectric constant K is inserted between its plates.
- The energy of a capacitor for a particular separation between the plates is the amount of work done in separating the two plates to that separation if they are made to touch to each other.
- The loss of energy when the two charged conductors are connected by a wire doesn’t depend on the length of the wire.
- When outer conductor is earthed,
- When inner sphere is earthed,
COMBINATION OF CAPACITORS
- In this combination, the positive plate of one capacitor is connected to the negative plate of the other.
- The charges of individual capacitor are equal.
- The potential difference is shared by the capacitors in the inverse ratio of their capacities
- The equivalent capacitance (C) between A and B is
- In this arrangement, +ve plates of all the condensers are connected to one point and negative plates of all the condensers are connected to the other point.
- The Potential difference across the individual capacitor is same.
- The total charge shared by the individual capacitor is in direct ratio of their capacities
- The equivalent capacitance between a and b is ceq = c1 + c2 + c3 + ……..+ cn
- The capacitance of a parallel plate capacitor having a number of slabs of thickness t1, t2, t3 …. and dielectric constant K1, K2, K3 …. respectively between the plates is
- When a number of dielectric slabs of same thickness (d) and different areas of cross-section A1, A2, A3 … having dielectric constants K1, K2, K3, …. respectively are placed between the plates of a parallel plate capacitor then the capacitance is given by
- When five capacitors are connected in wheatstone bridge arrangement as shown, such that, the bridge is balanced and C5 becomes ineffective. No charge is stored on C5. Therefore C1, C2 and C3, C4 are in series. The two series combinations are in parallel between A and C. Hence equivalent capacitance can be calculated.
RELATION BETWEEN THREE ELECTRIC VECTORS
EFFECT OF FILLING DIELECTRIC WITH BATTERY CONNECTED
EFFECT OF FILLING A DIELECTRIC IN A CAPACITOR AFTER DISCONNECTION OF BATTERY
CHARGING AND DISCHARGING A CAPACITOR
CHARGING A CAPACITOR
DURING THE PERIOD OF CHARGING
- The charge on the capacitor increases from ‘zero’ to the final steady charge.
- The potential difference developed across the capacitor opposes the constant potential difference of the source.
- The charge on the capacitor ‘grows’ only as long as the potential difference of source is greater than the potential difference across the capacitor. This transport of the charge from the source to the capacitor constitutes a transient current in the circuit.
- As the charge on the capacitor increases, more energy is stored in the capacitor.
- When the capacitor is fully charged, potential difference across the capacitor is equal to the potential difference of the source and the transient current tends to zero.
- At t = 0, q = 0.
- When t increases, q increases.
- At t = CR [‘CR’ has dimensions of time]
DISCHARGING OF A CAPACITOR
- the initial condition, q = Q0 at t = 0 and
- the final condition, q = 0 at ,
- If n small drops each having a charge q, capacity ‘C’ and potential V coalesce to form a big drop, then
- the charge on the big drop = nq
- capacity of big drop = n1/3 C
- potential of big drop = n2/3 V
- potential energy of big drop = n5/3 U
- surface density of charge on the big drop = n1/3 × surface density of charge on one small drop.
- Charged soap bubble : Four types of pressure act on a charged soap bubble.
- Pressure due to air outside the bubble PO, acting inwards.
- Pressure due to surface tension of soap solution PT, acting inwards.
- Pressure due to air inside the bubble, Pi, acting outwards.
- Electric pressure due to charging, Pe =, acting outwards.
- Force of attraction between the plates of a parallel plate capacitor =
- Uses of capacitor :
- In LC oscillators
- As filter circuits
- Tuner circuit in radio etc.
- The total energy stored in an array of capacitors (in series or in parallel) is the sum of the individual energies stored in each capacitor.
COMBINATION OF CAPACITOR : EQUIVALENT CAPACITANCE
SOME METHODS OF FINDING EQUIVALENT CAPACITANCE
SHARP POINT ACTION (CORONA DISCHARGE)
VAN DE GRAAF GENERATOR