Electric Charges And Fields

An electric dipole is placed at an angle of 30° with an electric field of intensity 2 × 10⁵ N/C. 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 length 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

An electric dipole is placed at an angle of 30° with an electric field of intensity 2 × 10⁵ N C⁻¹. It experiences a torque equal to 4 N m. Calculate the magnitude of charge on the dipole, if the dipole length is 2 cm.

Suppose the charges of a proton and an electron differ slightly. One of them is −e, the other is (e + Δe). If the net of the electrostatic force and the gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then Δe is of the order of [Given: mass of hydrogen mₕ = 1.67 × 10⁻²⁷ kg]

A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre

Two metal spheres, one of radius R and the other of radius 2R, have the same surface charge density σ. They are brought in contact and then separated. What will be the new surface charge densities on them?

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

A sphere encloses an electric dipole with charges ±3 × 10⁻⁶ C. What is the total electric flux across the sphere?

Two point charges A and B, having charges +Q and −Q respectively, are placed at a certain distance apart and the force acting between them is F. If 25% of the charge of A is transferred to B, then the force between the charges becomes

Two charged spherical conductors of radii R₁ and R₂ are connected by a wire. Then the ratio of the surface charge densities of the spheres (σ₁/σ₂) is

Polar molecules are the molecules:

A dipole is placed in a non-uniform electric field as shown. In which direction will it move?

Two point charges −q and +q are placed at a distance L apart, as shown in the figure. The magnitude of the electric field intensity at a distance R (R >> L) varies as

According to Gauss's law of electrostatics, the electric flux through a closed surface depends on:

A charge Q µC is placed at the centre of a cube. The flux coming out from any one of its faces will be (in SI unit):

If a conducting sphere of radius R is charged, then the electric field at a distance r (r > R) from the centre of the sphere would be (V = potential on the surface of the sphere):

If ∮ₛ E · dS = 0 over a closed surface, then:

An electric dipole with dipole moment 5 × 10⁻⁶ C m is aligned with the direction of a uniform electric field of magnitude 4 × 10⁵ N/C. The dipole is then rotated through an angle of 60° with respect to the electric field. The change in the potential energy of the dipole is:

Two identical charged conducting spheres A and B have their centres separated by a certain distance. Charge on each sphere is q and the force of repulsion between them is F. A third identical uncharged conducting sphere is brought in contact with sphere A first and then with B, and finally removed from both. The new force of repulsion between spheres A and B (radii of A and B are negligible compared to the distance of separation, so for calculating the force between them they can be considered as point charges) is best given as:

Which of the following statements are correct? A. Inside a conductor, the electrostatic field is zero. B. Electric field at the surface of a charged conductor does not depend on its surface charge density. C. The interior of a charged conductor can have no excess charge in the static situation. D. At the surface of a charged conductor, the electrostatic field must be normal to the surface at every point. E. The electrostatic potential is zero everywhere inside a charged conductor.