An electron is constrained to move along the central axis of a ring ofradius R having uniformly distributed charge q. Show that the electrostatic force exerted on the electron can cause itto oscillate through the centre of the ring with an angular frequency of `omega = sqrt((eq//4pi epsilon_(0)mR^(3)))`, where m is the mass of the electron `[sqrt((qe)/(4pi in_(0)mR^(3)))]`

A charge +Q is uniformly distributed over a thin ring of the radius R. The velocity of an electron at the moment when it passes through the centre O of the ring, if the electron was initially at far away on the axis of the ring is (m=mass of electron, K=1/(4pi epsi_(0)) )

A particle of mass m and charge -Q is constrained to move along the axis of a ring of radius a. The ring carries a uniform charge density +lamda along its length. Initially, the particle is in the centre of the ring where the force on it is zero. Show that the period of oscillation of the particle when it is displaced slightly from its equilibrium position is given by T=2pisqsqrt((2epsilon_0ma^2)/(lamdaQ))

An electric dipole is placed at a distance x from centre O on the axis of a charged ring of radius R and charge Q uniformly distributed over it. (a) Find the net force acting on the dipole (b) What is the work done in rotating the dipole through 180^(@) ? [(a) (aqQ)/(2piepsilon_(0))((R^(2)-2x^(2))/((R^(2)+x^(2))^(3//2))), (b) (aqQx)/(piepsilon_(0)(R^(2)+x^(2))^(3//2))]

A dence collection of equal number of electrona and positive ions is called netural plasma. Certain solids contianing fixed positive ions surroundedby free electrons can be treated as neytral plasma. Let 'N' be the numbrer density of free electrons, each of mass ' m '. When the elctrons are subjected to an eletric field, they are displaced relatively away from the heavy positive ions. if the electric field becomes zero, the electrons begin to oscillate about the positive ions with a natural angular frequency ' omega_(P)' which is called the plasma frequency. to sustain the oscillations, a time varying electric field needs to be applied that has an angular frequrncy omega , where a part of the energy is absorbed and a part of it is reflected. As omega approaches omega_(p) all the free electrons are set to resonance together and all the energy is reflected. this is the explaination of high reflectivity of metals. (2) Estimate the wavelength at which plasma reflection will occur for a metal having the density of electrons N~~ 4 xx 10^(27)m^(-3) . Taking epsilon_(0) = 10^(11) and mass m~~ 10^(-30) , where these quantities are in proper SI units.

The electric intensity Eat a point on the axis ofa ring of radius a at a distance x from its centre is given by (1)/(4piepsi_(0))(qx)/((a^(2)+x^(2))^(3//2)) where q is charge on ring. An electron is constrained to move along the axis of this ring. Show that the electron can perform oscillations whose frequency is given by omega=((eq)/(4piepsi_(0)ma^(3)))^(1//3) Where e is the charge on electron:

Which statement is true :- (i) A ring of radius R carries a uniformly distributed charge +Q. A point charge -q is placed on the axis of the ring at a distance 2R from the centre of the ring and released from rest. The particle executes a smiple harmonic motion along the axis of the ring. (ii) Electrons move from a region of higher potential to that of lower potential

A ring of radius R is having two charges q and 2q distributed on its two half parts. The electric potentiasl at a point on its axis at a distance of 2sqrt2 R from its centre is (k=1/(4piepsilon_0))

A charge q=10muC is distributed uniformly over the circumference of a ring of radius 3m placed on x-y placed with its centre art origin. Find the electric potential at a point P(0,0,4m)

A thin ring of 10 cm radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of 40pi "rad s"^(-1) about its axis, perpendicular to its plane. If the magnetic field at its centre is 3.8xx10^(-9)T , then the charge carried by the ring is close to (mu_(0)=4pi xx10^(-7)N//A^(2))