[2019EM/HMW-01]

1.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.

2. The electric field due to a line segment of length \(2a\), and carrying a uniform line charge \(\lambda\) at a distance \(d\) above the mid point is given by
\[E = \frac{1}{4\pi\epsilon_0} \, \frac{2\lambda a}{d \sqrt{d^2 +a^2}}\]
Using the above result find the electric field at a distance \(z\) above the
center of a square loop ( side \(2L\)) carrying a uniform line charge \(\lambda\).

3.Three charges are located on the circumference of a circle of radius \(R\) as shown in the figure below.  The two charges \(Q\) subtend an angle \(90^o\) at the centre of the circle. The charge \(q\) is symmetrically placed on the
circumference with respect to the charges \(Q\). What is the magnitude of \(Q\) if the electric field at the centre is zero?  

4. Use Gauss's law to find the electric field inside a uniformly charged
solid sphere of radius \(R\) and carrying charged density \(\rho\). State facts
other than Gauss's law which you might have used in your answer.

5. 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 = \(1.6\times10^{-16}\)]