In some old texts it is mentioned that `4pi` lines of force
. orginate form each unit positive charge. Comement on
. the statement in view of the fact that `4pi` is not an
. interger.

Two fixed, equal, positive charges, each of magnitude 5xx10^-5 coul are located at points A and B separated by a distance of 6m. An equal and opposite charge moves towards them along the line COD, the perpendicular bisector of the line AB. The moving charge, when it reaches the point C at a distance of 4m from O, has a kinetic energy of 4 joules. Calculate the distance of the farthest point D which the negative charge will reach before returning towards C.

There is another useful system of units, besides the SI/mKs. A system, called the cgs (centimeter-gram-second) system. In this system Coloumb's law is given by vecF =(Qq)/(r^(2)).hatr where the distance is measured in cm (= 10^(-2) m), F in dynes (= 10^(-5) N) and the charges in electrostatic units (es units), where 1 es unit of charge 1/(3) xx 10^(-9) C . The number [3] actually arises from the speed of light in vacuum which is now taken to be exactly given by c = 2.99792458 xx 10^8 m/s. An approximate value of c then is c = [3] xx 10^8 m/s. (i) Show that the coloumb law in cgs units yields 1 esu of charge = 1 (dyne) 1/2 cm. Obtain the dimensions of units of charge in terms of mass M, length L and time T. Show that it is given in terms of fractional powers of M and L. (ii) Write 1 esu of charge = x C, where x is a dimensionless number. Show that this gives: 1/(4piepsilon_(0)) = 10^(-9)/x^(2) (Nm^(2))/C^(2) with x=1/[3] xx 10^(-9) , we have 1/(4pi epsilon_(0)) = [3]^(2) xx 10^(9) (Nm^(2))/C^(2) or 1/(4pi epsilon_(0)) = (2.99792458)^(2) xx 10^(9) (Nm^(2))/C^(2) (exactly).

Answer carefully: (a) Two large conducting spheres carrying charges Q_(1) and Q_(2) are brought close to each other. Is the magnitude of electrostatic force between them exactly given by Q_(1),Q_(2)//4pi epsilon_(0)r^(2) , where r is the distance between their centres? (b) If Coulomb’s law involved 1//r^(3) dependence (instead of would Gauss’s law be still true ? (c) A small test charge is released at rest at a point in an electrostatic field configuration. Will it travel along the field line passing through that point? (d) What is the work done by the field of a nucleus in a complete circular orbit of the electron? What if the orbit is elliptical? (e) We know that electric field is discontinuous across the surface of a charged conductor. Is electric potential also discontinuous there? (f) What meaning would you give to the capacitance of a single conductor? (g) Guess a possible reason why water has a much greater dielectric constant (= 80) than say, mica (= 6).

If a line makes an angle (pi)/(4) with the positive directions of each of X-axis and Y-axis, then the angle that the line makes with the positive direction of the Z-axis is

The inverse square law in electrostatic is |F|=(e^(2))/((4pi epsi_(0))*r^(2)) for the force between an electrona nd a proton. The ((1)/(r)) dependence of |F| can be understood in quantum theory as being due to the fact that the particle of light (photon) is massless. If photons had a mass m force would be modified to |F|=(e^(2))/((4pi epsi_(0))r^(2))[(1)/(r^(2))+(lambda)/(r)] exp(-lambdar) where lambda=(m_(p)c)/(h) and h=(h)/(2pi) . Estimate the change in the ground state energy of a H-atom if m_(p) were 10^(-6) times the mass of an electron

The potential energy for a force filed vecF is given by U(x,y)=cos(x+y) . The force acting on a particle at position given by coordinates (0, pi//4) is

If the pair of lines sqrt(3)x^2-4x y+sqrt(3)y^2=0 is rotated about the origin by pi/6 in the anticlockwise sense, then find the equation of the pair in the new position.

There are two large parallel metallic plates S_(1) and S_(2) carrying surface charge densities sigma_(1) and sigma_(2) respectively (sigma_(1) gt sigma_(2)) placed at a distance d apart in vacuum. Find the work done by the electric field in moving a point charge q at distance a(a lt d) from S_(1) towards S_(2) along a line making an angle pi//4 with the normal to the plates.