Electric Charges & Fields

Two point charges of +4 μC and +9 μC are placed 0.3 m apart in air. Find the electrostatic force between them. (k = 9 × 10⁹ N·m²/C²)

How many electrons must be removed from a neutral conductor to give it a charge of +1.6 μC?

Point charges +Q and +4Q are fixed at the two ends of a line of length d. At what distance from the +Q charge should a third charge be placed (on the line, between them) so that the net force on it is zero?

Find the electric field intensity at a point 0.3 m from a point charge of 5 μC. (k = 9 × 10⁹ N·m²/C²)

A uniformly charged ring of radius 3 cm carries a charge of 1.25 nC. Find the electric field on its axis at a distance of 4 cm from the centre. (k = 9 × 10⁹ N·m²/C²)

A closed surface encloses a net charge of 4.425 × 10⁻⁹ C. Find the total electric flux through the surface. (ε₀ = 8.85 × 10⁻¹² C²/N·m²)

A charged conducting sphere has a uniform surface charge density of 8.85 × 10⁻⁸ C/m². Find the electric field just outside its surface. (ε₀ = 8.85 × 10⁻¹² C²/N·m²)

A uniformly charged non-conducting sphere of radius 10 cm carries a total charge of 1 nC. Find the electric field at a point 5 cm from its centre (inside the sphere). (k = 9 × 10⁹ N·m²/C²)

An infinitely long straight wire carries a uniform linear charge density of 2 × 10⁻⁶ C/m. Find the electric field at a perpendicular distance of 0.6 m from the wire. (k = 9 × 10⁹ N·m²/C²)

An infinite non-conducting plane sheet has a uniform surface charge density of 4.425 × 10⁻⁷ C/m². Find the electric field near the sheet. (ε₀ = 8.85 × 10⁻¹² C²/N·m²)

An electric dipole of moment 4 × 10⁻⁹ C·m is placed in a uniform electric field of 5 × 10⁴ N/C, making an angle of 30° with the field. Find the torque acting on it.

A dipole of moment 2 × 10⁻⁸ C·m is rotated from 0° to 60° with respect to a uniform field of 1 × 10⁵ N/C. Find the work done.

At the same distance r from a short electric dipole, the field on the axial line is E_axial and on the equatorial line is E_equatorial. Find E_axial/E_equatorial.

An electric dipole of moment 5 × 10⁻⁹ C·m is aligned parallel to a uniform field of 2 × 10⁴ N/C. Find its potential energy.

A charged particle of mass 4 g and charge 2 μC enters a uniform electric field of 1000 N/C, perpendicular to its initial velocity of 10 m/s, and travels a horizontal distance of 0.2 m through the field. Find its deflection in the direction of the field.

Two point charges in air repel each other with force F₀. If the space between them is now completely filled with a dielectric medium of dielectric constant K = 5, find the new force between them, in terms of F₀.

Three point charges +2 μC, +3 μC, and +4 μC are placed on a straight line at x = 0, x = 0.3 m, and x = 0.6 m respectively. Find the net force on the +3 μC charge due to the other two. (k = 9 × 10⁹ N·m²/C²)

A point charge q is placed exactly at one corner of a cube. Find the total electric flux through the entire (closed) cube.