A an electron is placed at the centre of the copper ring of problem 37. Show that if the electron is displaced a little, it will perform simple harmonic motion with a frequency `f=1/(2Pi)sqrt((eq)/(4piepsilon_0ma^3))`

A thin copper ring of radius a is charged with q units of electricity.An electron is placed at the centre of the copper ring .If the electron is displaced a little, it will have frequency

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:

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 0.1kg mass is suspended from a wire of negligible mass. The length of the wire is 1m and its crosssectional are is 4.9xx10^-7m^2 . If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency 140 rad s^-1 . If the Young's modulus of the material of the wire is nxx10^9 Nm^-2 , the value of n is

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

Two electrons each are fixed at a distance '2d'. A third charge proton placed at the midpoint is displaced slightly by a distance x (x lt lt d) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency : (m = mass of charged particle)

Two charges -q each are fixed separated by distance 2d. A third charge q of mass m placed at the mid-point is displaced at the mid-point is placed slightly by x (xltltd) perpendicular to the line joining the two fixed charges as shown in Fig. Show that q will perform simple harmonic oscillarion of time period. T = [(8pi^(3) in_(0) md^(3))/(q^(2))]^(1//2)

The displacement x(in metres) of a particle performing simple harmonic motion is related to time t(in seconds) as x=0.05cos(4pit+(pi)/4) .the frequency of the motion will be