Ls 1 - Electric Charges and Fields

Questions

Two identical charged spheres suspended from a common point by two massless strings of length l, are initially at a distance d(d<<l) apart because of their mutual repulsion. The charges begins to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then v varies as a function of the distance x between the spheres as?
A charged cloud system produces an electric field in the air near the earth's surface. A particle of charge -2×10^−19C is acted on by a downward electrostatic force of 3x10^−6N when placed in this field. The gravitational and electrostatic force, respectively, exerted on a proton placed in this field are (1) 1.64×10^−26N , 2.4×10^−16 N (2) 1.64×10^−26N, 1.5×10^−16 N (3) 1.56×10^−18N, 2.4×10^−16 N (4) 1.5×10^3 N , 2.4×10^−16 N

Two charges -3q and q are placed fixed on the x-axis separated by distance ‘d’. Where should a third charge 2q be placed such that it will not experience any force?
Two identical non conducting solid spheres of same mass and charges suspended in air from a common point by two non conducting massless strings of same length. at equilibrium at the angle between the strings is alpha the Spheres are now immersed in a dielectric liquid of density 800 kg metre cube and dielectric constant 21. If the angle between the strings remains the same after the immersion then...... a) electric force between the Spears remains unchanged b) electric force between the Spears reduces c) mass density of the spheres is 840 kg metre /cube d) tension in the strings remains the same
Three charges 4q, Q and q are in a straight line in the position of 0, l/2 and l respectively. The resultant force on q will be zero, if Q = _ _ _ _ _ (a) -q (b) -2q (c) -q/2. (D) 4q

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