Equipotential surfaces are defined as surfaces where the electric potential is constant. No work is done when moving a charge along these surfaces.

The electric potential outside a uniformly charged sphere is the same as that due to a point charge located at the center of the sphere.

The potential energy U of a system of two point charges is given by U = k * q1 * q2 / r.

The work done in moving a charge in an electric field is equal to the change in electric potential energy.

For capacitors in series, the equivalent capacitance C_eq is given by 1/C_eq = 1/C1 + 1/C2. Thus, 1/C_eq = 1/2 + 1/3 = 5/6, so C_eq = 6/5 = 1.2μF.

The equivalent capacitance of capacitors in series is given by 1 / (1/C1 + 1/C2).

At the midpoint, the electric fields due to both charges cancel each other out, resulting in a net electric field of 0.

The electric fields due to both charges at the midpoint cancel each other, resulting in a net electric field of 0.

The third charge must be placed between +q and -q, closer to -q to balance the forces.

The electric field is zero at a point closer to -q because the magnitudes of the fields due to both charges will be equal at that point.

Using Coulomb's law, F = k * |q1 * q2| / r². Let q be the charge, then 9 = (9 × 10^9) * (q²) / (1)². Solving gives q = 3μC.

U = k * q1 * q2 / r = (9 × 10^9) * (1 × 10^-6) * (1 × 10^-6) / 1 = 9 × 10^-3 J.

When brought into contact, the charges will redistribute equally, resulting in 0μC on each sphere.

When brought into contact, the charges will redistribute equally, resulting in 0μC on each sphere.

The electric fields due to both charges at the midpoint are equal and opposite, thus they cancel each other out, resulting in 0 N/C.

Potential energy U = k * q1 * q2 / r = (9 × 10^9 N m²/C²) * (5 × 10^-6 C)² / 1 m = 0.225 J.

When two identical spheres are brought into contact, they share their charges equally. Thus, they will have equal positive and negative charges after separation.

The potentials due to both charges at the midpoint cancel each other, so V = 0 V.

At the midpoint, the electric fields due to both charges cancel each other out, resulting in a net electric field of 0.

The electric potential at the midpoint is zero because the potentials due to +Q and -Q cancel each other out.

At the midpoint, the potentials due to both charges cancel each other out, resulting in a net potential of 0 V.

Inside a uniformly charged cylindrical shell, the electric field is zero due to symmetry, as the contributions from all parts of the shell cancel out.

Gauss's law states that the electric flux through a closed surface is proportional to the charge enclosed within that surface.

The capacitance C of a capacitor is directly proportional to the dielectric constant k. If k is doubled, C also doubles.

Capacitance C = ε₀A/d; if d is doubled, C is halved.

Capacitance, C = ε₀ * A / d. If d is halved, C doubles.

The electric field is directly proportional to the charge. Tripling the charge will triple the electric field.

In electrostatic equilibrium, the electric field inside a conductor is zero.

In electrostatic equilibrium, the electric field inside a conductor is zero.

In electrostatic equilibrium, the electric field inside a conductor is zero.