A spark passes though air when the potential gradient is `3xx10^(6)` volts per metre what must be the radious of an isoated metal sphere which can be changed to a potentiial of 3 million voilts before there are sparks in the air?
`["Hint":E= (Q)/(4piepsi_(0)r^(2))and V=(Q)/(4piepsi_(o)r), thereforeE=(V)/(r)]`

Air given way when there is a gradient of potential of 3xx10^(6) valts per matre . What is the maximum voltage to which a sphere of radius 1 cm can be charged ? What is the chage required ?

An isolated sphere of radius 5cm is charged to a potential of 159 Kv (Kilovoits). Find the electrostatic force per unit area of the surface. [Hint: Force per unit area =(sigma^(2))/(2epsi_(0))and V =(Q)/((4piepsi_(0)r))= (4pir^(2)sigma)/(4piepsi_(0)r)=(rsigma)/(epsi_(0))]

Calculate the change which must be placed on a sphere of radius 10 cm in order that the repulsion per square mertre of the surface may just balance the atmospheric pressure which is 1.013xx10^(5)Nm^(-2) ["Hint":P=(sigma)/(2epsi_(0))and Q=4pir^(2)sigma]

Show that the potential at a point of coordinates (x,y) with reference to the axis of the dipole as x -axis and the line perpendicular to the axis and passing through the centre of the dipole as y-axis is V = (1)/(4piepsi_(0)) , (px)/((x^(2) + y^(2))^(3//2)) and hence show that the components of the field along x- and y- axis are given by , E_(x) = (q)/(4pi epsi_(0)) , (2 x^(2) - y^(2))/((x^(2) + y^(2))^(5//2)) E_(y) = (p)/(4 pi epsi_(0)) , (3xy)/((x^(2) + y^(2))^(5//2)) [Hint : Find the value of cos theta and r in terms of x and y and substitute their values in the standard formula E_(x) = -(delV)/(delx) "and" E_(y) = -(delV)/(dely) ]

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

Calculate the volume of a sphere of radius (3.0pm0.1) cm, if the error quoted is the standard deviation in the measurement. [Hint: V=(4pi)/(3)r^(3),((deltaV)/(V))^(2)=3^(2)xx((deltar)/(r))^(2) ]

A coil of L=5xx10^(-3) H and R=18 Omega is abruptly supplied a potential of 5 volts . What will be the rate of change of current in 0.001 second? (e^(-3 .6)=0.0273)