The dipole moment p is defined as p = q * d.

The dipole moment p = q * d.

Dipole moment p = q * d = (1 × 10^-6 C) * (0.1 m) = 1 × 10^-7 C m.

Dipole moment p = q * d, if d is doubled, p also doubles.

Dipole moment p = q * d = (2 × 10^-6 C) * (0.1 m) = 2 × 10^-7 C m.

Torque τ = p × E = pE sin θ, where θ is the angle between p and E.

For a hollow cylinder, the electric field at a point outside is E = λ/(2πε₀r) using Gauss's law.

The electric field inside a hollow charged sphere is zero due to symmetry.

Inside a hollow charged sphere, the electric field is zero due to symmetry.

The electric field inside a hollow charged sphere is zero due to symmetry.

Inside a hollow charged sphere, the electric field is zero due to symmetry, as per Gauss's law.

Inside the cavity of a hollow conductor, the electric field is zero due to the shielding effect of the conductor.

Using Gauss's law for a cylindrical surface around the wire, the electric field E at a distance r is E = λ/(2πε₀r).

The electric field E between the plates of a parallel plate capacitor is given by E = V/d, where d is the separation between the plates.

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

The total electric flux through the surface is given by Gauss's law as Φ = Q/ε₀, and for a point charge at the center, it results in 4πQ/ε₀.

The electric potential V at a distance r from a point charge Q is given by V = kQ/r. Here, V = (9 x 10^9 Nm²/C²)(5 x 10^-6 C)/(2 m) = 1125 V.

According to Gauss's law, the total electric flux through a closed surface is Φ = Q_enc/ε₀. Here, Q_enc = Q, so Φ = Q/ε₀.

According to Gauss's law, the electric field inside a conductor in electrostatic equilibrium is zero.

The total flux through the cube is Q/ε₀. Since there are 6 faces, the flux through one face is Q/(6ε₀).

According to Gauss's law, the electric flux Φ = Q/ε₀ when a point charge Q is at the center of a spherical surface.

The electric potential inside a charged spherical conductor is constant and equal to the potential on its surface, which is Q/(4πε₀R).

The electric potential V on the surface of a charged spherical conductor is given by V = kQ/R.

The electric field outside a spherical charge distribution is given by E = Q/4πε₀r². At 2R, it becomes Q/4πε₀(2R)².

For a spherical shell, the electric field outside the shell behaves as if all the charge were concentrated at the center, so E = Q/(4πε₀R²).

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

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

The potential difference V = E * d = 200 N/C * 3 m = 600 V.

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

The electric field due to a charged plane sheet is directly proportional to the surface charge density. Therefore, if σ is doubled, E also doubles.