Electric fields from charge distributions

What you’ll practice

Electric fields from continuous charge distributions can look intimidating, but most problems reduce to smart setup: choose coordinates, exploit symmetry, and apply superposition correctly. You’ll practice turning a physical picture into the right differential element (dq) and field contribution (dE).

Each question uses 4 options and there’s no timer, so you can focus on reasoning and units rather than speed. Before you begin, pick how many questions you want to attempt and select a difficulty level that matches your current comfort.

Common pitfalls to avoid

Many wrong answers come from mixing up field and potential, choosing the wrong distance in the denominator, or forgetting vector direction. Another frequent slip is treating a non-uniform distribution like it’s uniform, or assuming symmetry where it doesn’t exist.

• Confusing E with V (vector vs scalar) and applying the wrong formula
• Using r instead of the correct separation distance from dq to the field point
• Dropping direction: forgetting components or sign conventions along axes
• Misusing symmetry (canceling components that don’t actually cancel)
• Forgetting the charge density factor (λ, σ, ρ) when writing dq

How the difficulty is balanced

Because the difficulty is mixed, you’ll see a blend of conceptual checks (direction, scaling, symmetry) and calculation-focused setups (integrals for rods, rings, disks, and infinite lines/planes). The progression is designed so easier items reinforce the core patterns, while harder ones test multi-step setup and careful component reasoning.

If you want a smoother run, start with fewer questions at an easier setting, then increase the count or difficulty once your setup steps feel automatic.