Suppose the charge of a proton and an electron differ slightly. One of them is $$-$$e, the other is (e + $$\Delta $$e). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (musch greater than atomic size) apart is zero, then $$\Delta $$e is of the order of
[Given : mass of hydrogen m_h = 1.67 $$ \times $$ 10$$-$$²⁷ kg]

An electric dipole is placed at an angle of 30^o with an electric field intensity 2 $$ \times $$ 10⁵ N C^$$-$$1. It experiences a torque equal to 4 N m. The charge on the dipole, if the dipole length is 2 cm, is

Two identical charged spheres suspended from a common point by two massless strings of lengths $$l$$, are initially at a distance d(d < < $$l$$) apart because of their mutual repulsion. The charges begin 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

If potential (in volts) in a region is expressed as V(x, y, z) = 6xy $$-$$ y + 2yz, the electric field (in N/C) at point (1, 1, 0) is