HARD
JEE Main/Advance
IMPORTANT
Earn 100

Four point charges + 8 μC , - 1 μC , - 1 μC and + 8 μC are fixed at the points, -272m ,-32m ,+32m and +272m  respectively on the y - axis. A particle of mass 6 ×10 -4 kg and of charge + 0.1 μC moves along the -x direction. Its speed at x=+ is v0. Find the least value of v0 for which the particle will cross the origin. Find also the kinetic energy of the particle at the origin. Assume that space is gravity-free. Given:1(4πε0) = 9×109 N m-2 C-2

Important Questions on Electrostatics

HARD
JEE Main/Advance
IMPORTANT
Three-point charges Q, 2Q and 8Q are to be placed on a 10 cm long straight line. Find the position where the charges should be placed such that the potential energy of this system is minimum. In this situation, what is the electric field at the position of the charge Q due to the other two charges? 
MEDIUM
JEE Main/Advance
IMPORTANT
A particle of charge -q and mass m moves in a circular orbit about a fixed charge +Q. Show that r3 α T2the law, is satisfied, where r is the radius of orbit and T is time period.
HARD
JEE Main/Advance
IMPORTANT
The field potential in a certain region of space depends only on the x-coordinate as V=ax3+b, where a and b are constants. Find the distribution of the space charge ρ(x).
HARD
JEE Main/Advance
IMPORTANT
The electric field strength depends only on the x and y coordinates according to the law, E= axi^+yj^x2+y2 where a is a constant, i^ and j^ are the unit vectors of the X and Y axes. Find the flux of the vector E through a sphere of radius R with its centre at the origin of coordinates. Using the above result, also calculate the total charge enclosed by the sphere.
MEDIUM
JEE Main/Advance
IMPORTANT

A positive charge is distributed in a spherical region with charge density ρ= ρ0 r for r  R (where ρ0 is a positive constant and r is the distance from centre). Find out electric potential and electric field at following locations.

(a) At a distance r from centre inside the sphere.

(b) At a distance r from centre outside the sphere.

HARD
JEE Main/Advance
IMPORTANT
Two point charges q and 2q are placed at a distance 6 m apart on a horizontal plane (xy plane). Find the locus of the zero potential points in the xy plane.
HARD
JEE Main/Advance
IMPORTANT
Two metallic balls of radii R1 and R2 are kept in vacuum at a large distance compared to their radii. Find the ratio of the charges on the two balls for which electrostatic energy of the system is minimum. What is the potential difference between the two balls for this ratio? Total charge of the balls is constant. Neglect the interaction energy. (Charge distribution on each ball is uniform)
HARD
JEE Main/Advance
IMPORTANT

A ball of radius R carries a positive charge whose volume density depends only on the separation r from the ball’s centre as ρ=ρ0 1  rR, where ρ0 is a constant. Assuming the permittivity of the ball and the environment to be equal to unity, find :

(i) The magnitude of the electric field strength as a function of the distance r both inside and outside the ball;

(ii) The maximum intensity Emax and the corresponding distance rm.