Physics Electric Charge and Field

Two point charge Q each are placed at a distance d apart. A third point charge q is placed at a distance x from mid-point on the perpendicular bisector. The value of x at which charge q will experience the maximum Coulomb's force is:

Two balls of same mass and carrying equal charge are hung by threads of length $l$ from a fixed support. At electrostatic equilibrium, assuming that angles made by each thread is small, the separation, $x$  between the balls is proportional to:

A charge q of mass m enters a region of electric field E = -E₀ĵ with a velocity v₀î + v₀ĵ at origin. Find the x coordinate where the charge hits the x axis again. (Neglect effect of gravity)

In the figure, a very large plane sheet of positive charge is shown. P1 and P2 are two points at distance $\mathcal{l}and2\mathcal{l}$ $$ from the charge distribution. If $\sigma$ $$ is the surface charge density, then the magnitude of electric fields E1 and E2 at P1 and P2 respectively are:

A short dipole of dipole moment P is placed along x – axis at a distance d from a long wire having uniform linear charge density +λ (wire is along y – axis) as shown. Find minimum work required to align this dipole along y axis (so that dipole moment P is along +y direction)

If ${\text{?}\mathrm{}}_{\mathrm{s}}\stackrel{?}{\mathrm{E}}\cdot \stackrel{?}{\mathrm{d}\mathrm{S}}=0$  over a surface, then:

Polar molecules are the molecules:

A big circular coil of 1000 turns, and average radius 10 m is rotating about its horizontal diameter at 2 rad ${\mathrm{s}}^{-1}$ . If the vertical component of earth's magnetic field at that place is $2*{10}^{-5}\mathrm{T}$ and electrical resistance of the coil is $12.56\mathrm{\Omega }$ , then the maximum induced current in the coil will be:

An electric dipole is placed at an angle of ${30}^{?}$ with an electric field of intensity $2*{10}^5{\mathrm{N}\mathrm{C}}^{-1}$ . It experiences a torque equal to $4\mathrm{N}\mathrm{m}$ . Calculate the magnitude of charge on the dipole, if the dipole length is $2\mathrm{c}\mathrm{m}$ .

An oil drop of radius 2 mm with a density 3gcm?³ is held stationary under a constant electric field 3.55 * 10? Vm?¹ in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will possess? Consider g = 9.81 m/s².