# Electric Potential Numerical Problems

Question 1
Calculate the amount of work done in assembling charge together to form a uniformly charged sphere.

Question 2
A charge Q is distributed over two concentric hollow spheres of radius r and R(>r) such that the surface densities of both the spheres are equal. Find the potential at the ir common centre.

Question 3
The potential in the region of space near the point P  (-2,4,6) is
$V=80x^2 + 60y^2$ V
(a) Find out the electric Field vector in the region
(b) Find out the Electric field vector at point P
(c) What is the value of potential at point P

Question 4
Two circular wire loops of radii .09 m (loop I) and .05 m(Loop II) are placed such that their axes coincide and their center are .12 m apart. Charge of 10-6 C is distributed uniformly on each loop. Find the potential difference between the centers of loop

Question 5
There are three charges on a straight line One Positive Charge q, Two Negative Charge -Q. Find the value of q/Q so that the entire system is in equilibrium? Will this equilibrium be stable?

Question 6
A thread of length L placed along the x-axis with one end at the origin is electrified uniformly along its length with a net charge Q.Find the potential and electric field strength at a point P which is at a distance r from the origin along the axis of rod beyond the rod.

Question 7
A point electric dipole having dipole moment p is placed in an external uniform electric field such that direction of dipole moment and electric field coincides. Find the radius of the sphere which forms one of the equipotential surfaces enclosing the dipole.

Question 8
Calculate the potential and field due to a dipole of dipole moment 3.5 x 10-11C/m at a distance .5m from it
1. on its axis
2. on its perpendicular bisector

Question 9
15 identical mercury drops are charged to a same potential of 5 Volts. Assuming the drops to be of spherical shape, find the potential of the large drop, made up of the combination of all the charged drops.

Question 10
Two charges -q each are separated by distance 2d. A third charge + q is kept at mid point O. Find potential energy of + q as a function of small distance x from O due to -q charges. Sketch P.E. v/s x and convince yourself that the charge at O is in an unstable equilibrium

Question 10
A point electric dipole having dipole moment p is placed in an external uniform electric field(E_0) such that directions of dipole moment and electric field coincides. Find the radius of the sphere which forms one of the equi-potential surface enclosing the dipole.
Ans
$r=(\frac {p}{4 \pi \epsilon _0 E_0})^{1/3}$

Question 11
Work done to move a charge along a closed path inside an electric field is always zero, using this fact, prove that it is impossible to produce an electric field in which all limes of force would be parallel lines and density of their distribution would constantly increase in a direction perpendicular to the lines of force

Question 12
Two conducting spheres of radii r1 & r2 are at same potential. What is the ratio of charges on the spheres?

Question 13
There are two identical particles each of mass m crying a charge Q. Initially one of them is at rest and another charge moves with velocity v directly towards free particle. Find the distance of closest approach.

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