By Gauss's law, the electric field inside a uniformly charged spherical shell is zero.

Inside a uniformly charged spherical shell, the electric field is zero due to symmetry.

By symmetry, the flux through one face of the cube is Q/6ε₀, as the charge is shared equally among the six faces.

For r > R, the electric field behaves as if all the charge were concentrated at the center, given by E = Q/(4πε₀r²).

Inside a uniformly charged spherical shell, the electric field is zero.

For a point outside the sphere, the electric field behaves as if all the charge were concentrated at the center, hence E = Q/(4πε₀r²).

The total electric flux through the Gaussian surface is given by Φ = Q/ε₀, where Q is the charge enclosed.

The electric flux through a closed surface is given by Φ = Q_enc/ε₀. Here, Q_enc = Q, so Φ = Q/ε₀.

According to Gauss's law, the total electric flux through a closed surface is equal to the charge enclosed divided by ε₀, thus Φ = Q/ε₀.

The electric field inside a non-conducting sphere with linearly increasing charge density varies linearly with radius.

At the center of a non-uniform spherical charge distribution, the electric field is zero due to symmetry.

The electric field inside a non-uniform charge distribution varies quadratically with radius due to the increasing charge density.

According to Gauss's law, the electric flux is directly proportional to the enclosed charge, so it doubles.

Capacitance C = Q/V; if Q is doubled and V remains constant, C must halve.

The energy stored in a capacitor is given by U = 1/2 * C * V^2. If the charge is doubled, the energy stored quadruples.

Capacitance is inversely proportional to the distance between the plates. If the distance d is doubled, the capacitance C becomes C/2.

Capacitance is inversely proportional to the distance between the plates. If the distance is halved, the capacitance doubles.

According to Coulomb's law, F ∝ 1/r^2. If r is doubled, F becomes F/4.

According to Coulomb's law, force is inversely proportional to the square of the distance. If the distance is doubled, the force reduces to one-fourth.

According to Coulomb's law, the force F between two charges is inversely proportional to the square of the distance. If the distance is halved, the force becomes four times greater.

According to Coulomb's law, F ∝ 1/r^2; halving the distance increases the force by a factor of 4.

Force F = E * q = 100 N/C * 5 × 10^-6 C = 0.0005 N = 0.5 N.

F = E * q = 200 N/C * 5 × 10^-6 C = 1 N.

The electric field is directed towards the charge, indicating that the charge is negative.

V = -E * d = -200 N/C * 3m = -600 V. The potential at B is 600 V lower than at A.

The electric field is zero when the vector sum of the electric fields due to all charges is zero, which occurs when there are equal and opposite charges.

The electric field due to an infinite plane sheet is constant and equal to E, regardless of the distance from the sheet.

The electric field due to an infinite plane sheet is constant and equal to E on both sides, thus the total field is 2E.

The fields due to the two sheets add up in the region between them, resulting in a total electric field of 2E.

Using E = k * |q| / r^2, we find q = E * r^2 / k = 1000 * 1^2 / (9 × 10^9) = 1μC.