[SNSet/EM-01001] Electromagnetic Theory --- Questions [QUE/EM-01011-016]

If an ink drop has a mass of \(50\times10^{-9}\) g and is given a charge of \(-200\times 10^{-15}\) C, find vertical displacement in an inkjet printer with 3keV deflection potential, 3mm plate separation and 15 mm deflection plate length. The nozzle ejects the drop with velocity 25 m sec\(^{-1}\) and leaving edge of the deflection plate is at a distance 15 mm from the paper.Source [Kraus p117]

A gold nucleus contains a positive charge equal to that of 79 protons. An \(\alpha\) particle, \(Z=2\), has kinetic energy \(K\) at points far away from the nucleus and is traveling directly towards the  charge, the particle just touches the surface of the charge and is reversed in direction. relate \(K\) to the radius of the gold nucleus. Find the numerical value of kinetic energy in MeV is the radius \(R\) is given to be \(5 \times10^{-15}\) m.

[ 1 MeV = \(10^6\) eV and 1 eV = \(1.6\times10^{-16}\)]

An electron is constrained to move along the axis of a ring of charge \(q\) and radius \(a\). Show that the electron can perform small oscillations along the axis of with time period given by \[T=\frac{1}{2\pi}\frac{4\pi\varepsilon_0 m a^2}{eq}\]

Two pith balls, each of mass 1.8 g, are suspended from the same point
by silk threads each of length 20 cm. When equal charge Q is given to
both the balls, they separate until the two threads become
perpendicular. Find the charge \(Q\) on each pith ball.

An alpha particle travels in a circular path of radius \(0.45\)m in a
magnetic field with \(B=1.2\)w/m\(^2\).
Calculate 
(i) its speed (ii) its period of revolution, and (iii) its kinetic
energy.
Mass of alpha particle = \(6.64424. 10^{-27}\)kg \(\approx 4\times M_p= 4\times938.27\) MeV.

An alpha particle travels in a circular path of radius \(0.45\)m in a magnetic field with \(B=1.2\)w/m\(^2\). Calculate
(i) its speed
(ii) its period of revolution, and
(iii) its kinetic energy.
[Mass of alpha particle =  \(6.64424. 10^{-27}\) kg =3727.4 MeV.]