REVISION PLUS- ELECTROSTAT

REVISION –PLUS ELECTROSTATICS LS-17/AS 3rd Feb 2010 7.00-8.00p.m. : REVISION –PLUS ELECTROSTATICS LS-17/AS 3rd Feb 2010 7.00-8.00p.m. ELECTROSTATICS ELECTRIC FIELD ELECTRIC POTENTIAL

ELECTROSTATIC CHARGES : ELECTROSTATIC CHARGES Electrostatics stands for static electricity involving study of charges at rest. These charges are developed on insulators when they are rubbed against each other. The charges are produced due to actual transfer of electrons.

PROPERTIES OF CHARGES : PROPERTIES OF CHARGES . Two important properties of charges are Quantization and Conservation. The quantization means that charge can exist only as integral multiple of electronic charges. where n is an integer.

PROPERTIES OF CHARGES : PROPERTIES OF CHARGES The conservation of charge means that on an isolated system ,total electric charge always remains constant. Obviously, the charges can be created only in equal and unlike pairs.

COULOMBS LAW : COULOMBS LAW

COULOMBS LAW : COULOMBS LAW . Like charges repel and unlike charges attract each other with a force F governed by Coulomb’s law

COULOMBS LAW : COULOMBS LAW and charges are unlike charges

COULOMBS LAW : COULOMBS LAW . where q1,q2 are the charges held r distance apart in vacuum; is force on q2 by q1 and is vector pointing q1 to q2. where is absolute electrical permittivity of free space.

COULOMBS LAW : COULOMBS LAW When the same charges are separated by the same distance in medium of relative permittivity or K, the force between the charges becomes:

. : . . SUPERPOSITION PRINCIPLE To find total force on a given charge q0 due to any number of charges q1, q2 ….qn we use superposition principle, according to which i.e. vector sum of forces due to individual charges would give us the total force.

. : . . ELECTRIC FIELD Electric field intensity at any position(r) is defined as where is total force experienced by a small positive test charge q0. The direction of is the direction along which the positive test charge would try to move, if free to do so.

. : . . ELECTRIC FIELD Electric field intensity at a point distant r from a point charge q in air is Electric field intensity due to a group of charges is obtained by applying superposition principle. The SI unit of is NC-1.

. : . . ELECTRIC LINE OF FORCE An electric line of force is a path, straight or curved, such that tangent to the path a any point gives us the direction of electric field intensity at that point. No two electric lines of force can intersect each other.

. : . . ELECTRIC DIPOLE Two equal and opposite charges separated by a small distance are said to form an electric dipole. Many of the atoms/molecules are dipoles. For all your Physics Problems Call me at……………9814123832 Email ………………. hksidhuinstitute@gmail.com

ELECTRIC DIPOLE MOMENT : ELECTRIC DIPOLE MOMENT Every dipole is associated with a DIPOLE MOMENT whose magnitude is equal to the product of the magnitude of either charge(q) and the distance between the charges,i.e. The direction of is from negative charge to positive charge. It is measured in coulomb-metre. Every dipole has an electric field around it.

. : . ELECTRIC DIPOLE Field intensity at any point on axial line of electric dipole is, where r is distance of the point from the centre of dipole

. : . . ELECTRIC DIPOLE If the point lies on equatorial line of dipole at the same distance r, then .

. : . . TORQUE ON ELECTRIC DIPOLE When an electric dipole of moment is held at an angle ? with the direction of a uniform electric field E, a torque acts on the dipole, given by: in magnitude. This torque tries to align the dipole in the direction of the field, reducing angle ? to zero.

POTENTIAL ENERGY IN ELECTRIC DIPOLE : POTENTIAL ENERGY IN ELECTRIC DIPOLE To orient the dipole at any other angle with ,work has to be done on the dipole, which is stored as P.E.of dipole given by:

. : . . ELECTROSTATIC POTENTIAL . Electrostatic potential difference between two points B and A in an electrostatic field is the amount of work done in carrying unit positive test charge from A to B (against the electrostatic force of the field) along any path between the two points, i.e.,

. : . . ELECTROSTATIC POTENTIAL If A is at =0, we may write,

ELECTROSTATIC POTENTIAL : ELECTROSTATIC POTENTIAL This means electrostatic potential at a point in the electrostatic field is the amount of work done in moving a unit positive test charge from infinity to that point, against the electrostatic forces, along any path. Electrostatic potential is a scalar and it is measured in volt.

. : . . ELECTROSTATIC POTENTIAL Electric potential at a point distant r from a point charge q is, Electric potential at a point due to a group of charges and due to continuous charges distribution can be calculated similarly using the superposition principle.

. : . . ELECTROSTATIC POTENTIAL Further, electric field intensity at any point is negative rate of change of potential with distance at the point i.e. . An equipotential surface is that at every point of which electric potential is the same. Equipotential surfaces are always perpendicular to the field lines.

. : . . ELECTROSTATIC POTENTIAL ENERGY Electric potential energy of a system of point charges is the total amount of work done in bringing the various charges to their respective positions from infinitely large mutual separations.

ELECTROSTATIC POTENTIAL ENERGY : ELECTROSTATIC POTENTIAL ENERGY Electric potential energy of a system of two point charges is given by: S.I.Unit of U is joule. Another convenient unit of energy is electron volt(eV),where

. : . . ELECTROSTATIC FLUX Electric Flux over an area in an electric field represents the total number of electric field lines crossing this area. It is represented by Electric flux is a scalar quantity, and is measured in

. : . . GAUSS LAW According to Gauss’s theorem in electrostatics, total normal electric flux over a closed surface S in vacuum is time the total charge (Q) contained inside the surface.

GAUSS LAW : GAUSS LAW Coulomb’s law of force can be obtained from Gauss’s theorem. This theorem can be used for calculating electric field intensity due to highly symmetric charge distributions.

. : . . CAPACITANCE CONDUCTORS are the materials which possess a large number of free charge carriers whereas Insulators or dielectrics possess a negligibly small number of free charge carriers.

CONDUCTOR IN ELECTRIC FIELD : CONDUCTOR IN ELECTRIC FIELD When a conductor is placed in an external electric field, net electric field in the interior of a conductor is zero, there is no charge in the interior of the conductor i.e. charge always resides on the outer surface of the conductor.

. : . . CONDUCTOR IN ELECTRIC FIELD The surface of the conductor is an equipotential surface and electric field over a charged conductor is perpendicular to the surface of the conductor at every point.

. : . . CAPACITANCE Capacitance (C) of a capacitor is the ratio of charge (Q) given to conductor and the potential (V) to which it is raised I.e. C = Q/V. The value of C depends on size, shape and relative position of two coatings Plates of the capacitor.

CAPACITANCE : CAPACITANCE Capacity of an isolated spherical conductor of radius r in vacuum is, Capacity of a parallel plate capacitor with air as dielectric is Where A is area of each plate and d is distance between them.

. : . . CAPACITANCE When the insulating medium separating the two conductors in a capacitor is other than air, its capacity becomes K times the capacity in air. Here, K is dielectric constant or relative electrical permittivity of the medium. For mica, K =3 to 6 for paper K = 3.5, for water, K = 81, for ebonite, K = 2.7 and for glass, K varies from 3 to 4.

. : . . CAPACITANCE When condensers are grouped in series, total capacity C, is given by In parallel grouping, total capacity is sum of the individual capacities i.e.

. : . . CAPACITANCE .Work done in charging a capacitor is stored in it in the form of ELECTROSTATIC ENERGY, given by when Q is coulomb, V in volt and C in farad, energy E is in joule.

. : . . CAPACITANCE When two capacitors charged to different potentials are connected by a conducting wire, charge flows from the one at higher potential to the other at lower potential till their potentials become equal. The equal potential is called COMMON POTENTIAL (V),where

. : . . CAPACITANCE In sharing of charges, there is absolutely no loss of charge. Some energy is, however, lost in the process which is given by:

. : . . CAPACITANCE Dielectrics are of two types: Non polar and polar. The non polar dielectrics Benzene, methane)etc,are made up of non polar atoms/molecules, in which the centre of positive charge coincides with the centre of negative charge of the atom/molecule.

CAPACITANCE : CAPACITANCE The polar dielectrics are made up of polar atoms/molecules, in which the centre of positive charge does not coincide with the centre of negative charge of the atom/molecule. A non polar dielectric can be polarized by applying an external electric field on the dielectric.

. : . . CAPACITANCE The effective electric field in a polarized dielectric is given by where is strength of external field applied and is intensity of induced electric field set up due to polarization.

. : . . CAPACITANCE Capacitance of a parallel plate capacitor with a conducting slab of thickness t is given by: Capacitance of a parallel plate capacitor with a dielectric slab of thickness t is given by

VAN DE GRAFF GENERATOR : VAN DE GRAFF GENERATOR . A Van de Graff generator is a powerful machine used for generating high positive potentials = volt. It is based on the action of sharp points and the property that charge always resides on the outer surface of a hollow conductor. Such high positive potentials are needed for accelerating positive ions.

. : . . ELECTROSTAT IMPORTANT Q’S Define electric flux. Write its S.I.unit. A charge q is enclosed by a spherical surface of radius R. If the radius is reduced to half, how would the electric flux through the surface change ?

. : . . ELECTROSTAT IMPORTANT Q’S Draw 3 equipotential surfaces corresponding to a field that uniformly increases in magnitude but remains constant along Z-direction. How are these surfaces different from that of a constant electric field along Z-direction ?

. : . . ELECTROSTAT IMPORTANT Q’S A parallel plate capacitor is charged by a battery. After some time the battery is disconnected and a dielectric slab of dielectric constant K is inserted between the plates. How would (i) the capacitance, (ii)the electric field between the plates and (iii) the energy stored in the capacitor, be affected? Justify your answer.

. : . . ELECTROSTAT IMPORTANT Q’S State Gauss’s theorem in electrostatics. Apply this theorem to derive an expression for electric field intensity at a point near an infinitely long straight charged wire.

ELECTROSTATICS EXPECTED QUESTIONS : ELECTROSTATICS EXPECTED QUESTIONS Q Three points A, B and C lie in a uniform electric field E of 5 x 103 NC-1 as shown in the figure. Find the potential difference between A and C.

ELECTROSTATICS IMPORTANT QUESTIONS : ELECTROSTATICS IMPORTANT QUESTIONS Ans. Let the angle BAC be equal to ?. Using relation, Between points A and C, we have

ELECTROSTATICS IMPORTANT QUESTIONS : ELECTROSTATICS IMPORTANT QUESTIONS . Two identical equally charged bodies A and B are kept at a certain distance. A third identical neutral body is first touched with A and then with B. Find the ratio of initial and final forces experienced by the bodies A and B. For all your Physics Problems Call me at……………9814123832 Email ………………. hksidhuinstitute@gmail.com

ELECTROSTATICS IMPORTANT QUESTIONS : ELECTROSTATICS IMPORTANT QUESTIONS Ans. The initial force F between bodies A and B. each carrying charge q and kept r distance away from each other is when neutral body C is touched with A, its new charge

ELECTROSTATICS IMPORTANT QUESTIONS : ELECTROSTATICS IMPORTANT QUESTIONS On touching C with body B the new charge on B will be

ELECTROSTATICS IMPORTANT QUESTIONS : ELECTROSTATICS IMPORTANT QUESTIONS

. : . . ELECTROSTAT IMPORTANT Q’S A point charge q is placed at O as shown in the figure. Is V positive or negative when (i) q>O;(ii)q < O ? Justify your answer.

. : . . ELECTROSTAT IMPORTANT Q’S Using Gauss’s theorem, show mathematically that any point outside the shell, the field due to a uniformly charged thin spherical shell is the same as if the entire charge of the shell is concentrated at the centre. Why do you expect the electric field inside the shell to be zero according to this theorem ?

ELECTROSTAT IMPORTANT Q’S : ELECTROSTAT IMPORTANT Q’S Q.4. Find the electric flux linked with the square as shown in the figure below.

ELECTROSTAT IMPORTANT Q’S : ELECTROSTAT IMPORTANT Q’S Ans. If we complete the cube, we observe that only charge is enclosed by the cube, as inside charge. Using Gauss’s theorem total electric flux coming out of the cube of side a will be,

ELECTROSTAT IMPORTANT Q’S : ELECTROSTAT IMPORTANT Q’S As there are six square inside a cube so the flux linked with a single squares will be.

ELECTROSTAT IMPORTANT Q’S : ELECTROSTAT IMPORTANT Q’S Q. A parallel plate capacitor, each with plate area A and separation d is charged to a potential difference V. The battery used to charge it is then disconnected. A dielectric slab of thickness d and dielectric constant K is now placed between the plates. What change, if any, will take place in (a) charge on the plates (b) electric field intensity between the plates. (c) capacitance of the capacitor.

ELECTROSTAT IMPORTANT Q’S : ELECTROSTAT IMPORTANT Q’S Ans. (a) As after charging the battery is removed, so the charge on the capacitor remains unchanged. (b) The electric field intensity is reduced by the factor K, as (c) The capacitance will increase by factor K as

ELECTROSTAT IMPORTANT Q’S : ELECTROSTAT IMPORTANT Q’S Q.8. A parallel plate capacitor has its two plates kept 0.02 m apart. A dielectric slab of thickness 0.01m is introduced between the plates with its faces parallel to them. The distance between the plates is readjusted to make the capacity of the capacitor (2/3)rd of its original value. Given that the dielectric constant of the slab equals 5, find the new distance between the plates.

ELECTROSTAT IMPORTANT Q’S : ELECTROSTAT IMPORTANT Q’S Ans. Given that, d = 0.02 m, t = 0.01 m,

ELECTROSTATICS EXPECTED QUESTIONS : ELECTROSTATICS EXPECTED QUESTIONS Substituting the values, we get

. : . . ELECTROSTAT IMPORTANT Q’S The given graph shows the variation of charge q verses potential difference V for two capacitors C1 and C2. The two capacitors have same plate separation but plate area of C2 is double than that of C1 . Which of the lines of the graph correspond to C1 and C2 and why ?

. : . . ELECTROSTAT Q’S Two point charges Are located 20 cm apart in vacuum(a) What is the electric field at the mid point O of the line AB joining the two charges ?(b) If a negative test charge of magnitude 1.5 x 10-9C is placed at the point, what is the force experienced by the test charge ?

. : . . ELECTROSTAT Q’S Ans.Here, Electric field is the force on unit positive charge(+1C)at O.

. : . . ELECTROSTAT Q’S Force on negative charge Q=-1.5x109C at O will be F=qE=-1,5x10-9(5.4x106)N F = -8.1 x 10-3N ; along OA. For all your Physics Problems Call me at……………9814123832 Email ………………. hksidhuinstitute@gmail.com

ELECTROSTAT Q’S : ELECTROSTAT Q’S . . Consider a uniform electric field E = 3x103 N/C. (a) What is the flux of this field through a square of 10 cm on a side whose plane is parallel to the yz plane ? (b) What is the flux through the same square if the normal to its plane makes a 600 angle with the x-axis?

ELECTROSTAT Q’S : ELECTROSTAT Q’S . Ans. Here, i.e.,field is along + direction of X-axis ? surface area, s=(10cm)2=102cm2=102x10-4m2=10-2m2 (a) When plane is parallel to yz plane, ?=00 (b) When normal to the plane makes an angle of 60o with X-axis, the ?=60o

Slide 71 : For all your Physics Problems Call me at……………9814123832 Email ………………. hksidhuinstitute@gmail.com