Conducting Sphere: Charge resides only on the surface. Insulating Sphere: Charge can be distributed throughout the volume.

λ: Charge per unit length (Q/L), used for lines. σ: Charge per unit area (Q/A), used for sheets.

1. Break the total charge Q into tiny pieces dq.
2. Find the electric field dE due to each piece dq using $dE = k \frac{dq}{r^2} \hat{r}$.
3. Integrate dE to find the total electric field E.

1. Choose a Gaussian surface that matches the symmetry of the charge distribution.
2. Calculate the electric flux through the Gaussian surface, $E \oint dA$.
3. Calculate the enclosed charge, $q_{enc}$.
4. Apply Gauss' Law: $E \oint dA = \frac{q_{enc}}{ε_0}$ and solve for E.

1. Find an expression for the electric field E, often using Gauss' Law.
2. Plug the expression for E into the integral: $ΔV = -\int E \cdot dl$.
3. Evaluate the integral with appropriate limits of integration.

Express dq in terms of dy using the linear charge density λ: $dq = λ dy$.

Choose a Gaussian surface that matches the symmetry of the charge distribution.

Outside the sphere, the electric field decreases proportionally to the inverse square of the radius.

The electric field increases linearly with the distance from the center until r = R (the radius of the sphere).

The electric potential is constant inside the conductor.

The electric field is zero.