In a region, the potential is represented by V(x, y, z) = 6x – 8xy – 8y + 6yz, where V is in volts and x, y, z are in metres. The electric force experienced by a charge of 2 coulomb situated at point (1, 1, 1) is :-

For an electric dipole in a non-uniform electric field with dipole moment parallel to direction of the field, the force F and torque τ on the dipole respectively are ___________.
Fill in the blank with the correct answer from the options given below.

Two charged particles, placed at a distance d apart in vacuum, exert a force F on each other. Now, each of the charges is doubled. To keep the force unchanged distance between the charges should be changed to _____________.
Fill in the blank with the correct answer from the options given below.

An electric dipole is placed at an angle of 30° with an electric field of intensity . It experiences a torque equal to 4 Nm. Calculate the magnitude of charge on the dipole, if the dipole length is 2 cm.

If over a surface, then :

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 υ. Then υ varies as a function of the distance x between the spheres, as

A dipole is placed in an electric filed as shown. In which direction will it move?

In a region, the potential is represented by V(x, y, z) = 6x – 8xy – 8y + 6yz, where V is in volts and x, y, z are in metres. The electric force experienced by a charge of 2 coulomb situated at point (1, 1, 1) is :-

An electric dipole is placed as shown in the figure.
The electric potential (in 10² V) at point P due to the dipole is

Two parallel infinite line charges with linear charge densities are
placed at a distance of 2R in free space. What is the electric field mid-way between the two
line charges?