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Special Techniques By: Jay Pandya 1. A dipole p is placed radially at a distance d from the centre of a grounded conducting sphere of radius r(<d).What is the magnitude of dipole moment compared to p ? a) More b) Less c) Equal 2. Certain charge is distributed over a circle according to the law q = q0cost where q is the surface charge density and t is the angle measured from the x axis. What is direction of total dipole moment? a) Along x axis b) Along y axis c) Along the line y=x d) Along the line y=-x 3. Two charges q1 and q2 are placed at (0,0,a) and (b,0,0) respectively. Find the average potential due to both the charges over the surface of a sphere of radius r (<a<b) which is centred at origin. a) kq1/a b) kq2/b c) kq1/a + kq2/b d) kq1/b + kq2/a 4. For the above problem if a<r<b what is the average potential over the surface of sphere? a) kq1/a + kq2/b b) kq1/r + kq2/b c) kq1/a + kq2/r d) kq1/r + kq2/r 5. The potential of four charges q(0,0,d) , 2q(d,0,0) ,-q (0,0,-d) , -2q(-d,0,0) will have the major contribution from which multipole term a) Monopole term b) Dipole term c) Quadrupole term 6. Two charges q & 2q placed at a distance d and 2d respectively from a grounded conducting plane. What is magnitude of force experienced by the charge q? a) 2kq2/d2 b) 2kq2/d2 + kq2/(2d)2 c) 2kq2/d2 + kq2/(2d)2 + 2kq2/(3d)2 d) None of these 7. A charge q is placed at a distance d from the centre of a grounded conducting spherical shell of radius r(<d) . What is the force experienced by the charge q? 8. Prove using uniqueness theorem that electric field in an empty cavity of a conductor is zero. 9. If a point charge q is held a distance d above a grounded conducting plane then what is the potential in the region above the plane?