1 Three changes and are located in x-y plane at positions (0, a), (0, — a) and (b, 0) respectively. Find the net electrostatic force on
2. Four identica1 charges are fixed at the corners of a square of side ‘a’. A fifth point charge ‘–Q’ lies’a distance ‘z’ along the line perpendicular to the plane of, the square. Show that for z << a the motion Of -Q is simple harmonic. What would be the period of motion, if the mass of-Q is m? (Neglect the gravitational force).
3.A charged wire of length L lies along x-axis in such away that its linear charge density λ=bx3 is where ‘b’ is constant. Determine the total charge on the wire.
4. A uniformly charged wire, lenear chargé density λ , is laid in the form of a semicircle of radius R. Find the electric field generated by the semicircle at the centre.
5. A tiny mass m with charge q .is attached to. an infinite sheet of charge densityσ a by means of an insulating mass less cord of length l.
(i) Specify thé signs of the charge q and such that the cord is taut.
(ii) Show that if the mass is pulled slightly in a direction parallel to the plane and then released, the mass excecutes simple harmonic motion with
6. Consider Earth to be a ball, of radius Rand mass M let the charge of earth be Q
(i) What must be t maximum mass m of an object carrying an electric charge equà1 to the proton and moving in the electric field of the Earths so that the object may escape earths gravitational pull and off into outer space?
(ii)What can’ be the maximum charge Qmax, carried by a dust particle (an object) and how can such a charge be imparted to the object?
7, Electrically charged’ drops of mercury fall an altitude h into a spherical metal vessel of radius R in the upper part of which there is a small opening. The mass of each drop is m and the charge on he drop is Q. What, will be the number ’n’ of the last drop that can still enter sphere
8. Two equal point charges are fixed at x = -a and x = + a on the x-axis.’ Another point charge Q is placed at the Origin. Find the change in electrical energy of Q (approx), when it is displaced by a small distance along the x-axis.
9. ‘A proton of mass ‘m’ approaches from a very large distance towards a free proton with a velocity V0 along the straight line joining their centres. Find the closest distance of approach between the two protons.
consider a small element dl on the ring,. This element creates a field dE which makes an angle at the centre as shown in figure. The y-components of field due to these symmetric elements cancel out, and x-components remain as