## some electrostatics questions

these are some questions which I coudnt get

Q1 :
A thick shell with inner radius R and outer radius 3R has uniform volume charge density ''sigma" it has a spherical cavity of radius R, what is the field at the centre of the cavity... The cavity is tangential.

shoudnt we find the field inside the cavity by the whole shell and then subtract the field because of the cavity alone? Note that the shell is not a conducting one.

Q2 : Two concentric conducting shell having radii a and b are charged to q1 and q2. the potential difference between shell 1 and shell 2 is ?

since it is conducting ( both are ) the potential between the two should be kq2/b right? because the potential inside is the same as the potential at the surface??
but the answer is kq1(1/a - 1/b) ..

Q3 there are thre concentric charged spherical shells A, B, C having charge densities sigma, -sigma ,sigma and radii a , b , c . if V(A) = V(C), b = ?

Q4: There is an infinite line charge of charge density sigma. A charged particle from a distance 3R is moved parallel to the line charge from points A to B, then it undergoes a semicricular path of radius R and reacches point C . Find the work done in the entire process.(The line charge and the path ABC lies in the same plane)

in this AB is one of the equipotential regions.. so no work done while moving from A to B. But there is a work done from B to C right? E for line charge is E = sigma/(epslion*2*pi*r), so the potential difference can be found by finding the negative integral of E with r with limits from 3R to R.. so we'll get -sigma*log3/(2*pi*eplison) but the answer here says zero ...

Q5: A point charge Q is located at the centre of a hollow spherical conductor of iner radius R1 and outer radius R2 the conductor is uncharged initially. the potential at inner surface will be...
now becuase Q is inside , it wil induce -Q at first shell, which wil induce +Q at outer shell, so the potential at inner surface will be the sum that is (-Q/R1 +Q/R2) *k but answer is kQ/R2

Q6 there is a uniformly charged sphere of radius R and charge Q. there is a tunnel in the sphere from one point of surface A to other point of surface B. Distance of closest point of tunnel from centre is R/2 . Surface of tunnel is smooth and made from insulated material. A charged particle of charge q and mass M is thrown in to the tunnel from A. What is the minimum velocity with which it is thrown so that it reached B. THe tunnel is circular.

Q7 there is a sphere of radius R with spherical cavity of radius R/2, the cavity is tangential.. Charge on spehere is Q which is uniromly distributed in non cavity volume. Centre of sphere is O and centre of cavity is C. A negatively charged particle of -q is moved from A to B which are diametrically opposite points of the cavity but B is not in the circumference of the cavity. The angle between AC and OC is 60 degree. what is the work done?

Please help! I tried solving these Questions yesterday, but I cant get any answer that is mentioned in the options..