IIT JEE Advanced & Mains Physics 2018 : Electricity : Rank file / expected questions : II

IIT JEE Advanced & Mains Physics 2018 : Electricity : Rank file / expected questions / Physicsmynd Elite Series  /  Page  II 

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10 .  A soap bubble of radius 1 cm , which is at a potential of 90 volts ,  collapses to a drop of radius 1 mm . Find the change in its electrostatic energy?

11.From a  sphere of uniform charge density \rho and radius R ,a small spherical hollow region of radius r is cut out at a distance d from the center of it .
(a) What is the  field E at the center of the hollow sphere ?

12 .In addition ,also find the potential \phi at above stated point.

13 . Suppose ,in the above case , a particle of charge q is moved from infinity to the center of the spherical shell through the cut out hole . Find the work needed ? [take the thickness of the shell to be t .]

14 .Find the  the electric field and potential at the center of a ring of radius r whose net  charge +Q is uniformly distributed on it. 

15.  Calculate the point(s) on the axis of a charged ring where the electric field is maximum.

16.Figure below shows the discharge curve of a Capacitor . From the graph the valve of time [ t ] when \frac {Q}{{Q}_{{0}}}=10 is-

A ] t=2.303\tau

B ] t=2.400\tau

C ] t=1.303\tau

D ] t=3\tau

17 ]   Drift Velocity

The primary charge carriers in sea water  are {Na}^{+} and {Cl}^{-} ions. Consider a non conducting pipe of 3 meters connected to a 15 volt battery at it’s both ends by an electrode.This pipe is then filled with seawater..Find the average drift velocity of the ions, in cm/s?

Note : The resistivity of seawater is about 25{\Omega}-m and there are about 3}\times{10}^{20}/{cm}^{3} of each ions .

18 ] Consider the following arrangement .-

An air-filled parallel-plate capacitor of area A , with plates a and b are kept on a smooth surface in such a manner ,that it’s one end is fixed and the other is  connected to a spring having a force constant k .The charges on the plates are respectively  Q + and  Q – .Then the expansion of the spring is – 

A ] x=\frac {{Q}^{{2}}}{2kA{\epsilon }_{{0}}}

B ] x=\frac {{Q}^{{2}}}{kA{\epsilon }_{{0}}}

C ] x=\frac {{Q}^{{3}}}{2kA{\epsilon }_{{0}}} 

D ] x=\frac {{Q}^{{2}}}{2A{\epsilon }_{{0}}}

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