Introduction
Electric field and potential problems often require careful application of fundamental equations, along with systematic reasoning. This section presents strategies to approach problems effectively.
Step 1: Visualize the Problem
Sketch the physical setup: charges, fields, equipotentials, or capacitors. Diagrams help clarify directions and symmetries.
Step 2: Identify What is Given and Required
List known values (charge, distance, voltage, capacitance, etc.) and clearly state the target quantity (field strength, potential difference, stored energy, etc.).
Step 3: Recall the Relevant Equations
- Coulomb’s Law: F = k q₁q₂ / r²
- Electric Field: E = F / q = kQ / r²
- Electric Potential: V = kQ / r
- Capacitance: C = Q / V
- Energy in Capacitors: U = ½ CV²
Step 4: Check Symmetry
In many cases, symmetric charge distributions simplify calculations. Use superposition to handle multiple sources of electric field or potential.
Step 5: Perform Calculations Carefully
Work step by step. Carry units throughout to minimize mistakes. Keep track of vector directions when working with fields.
Step 6: Evaluate the Result
Ask whether the answer is physically reasonable. For instance, does the magnitude make sense? Are the units correct? Is the direction of the field logical?
Example Strategy
Example: Two charges, +3 μC and −2 μC, are separated by 0.4 m. Find the electric field at a point midway between them.
Strategy:
- Sketch the setup and mark the midpoint.
- List knowns: q₁ = +3 μC, q₂ = −2 μC, r = 0.2 m (from midpoint to each charge).
- Use E = kQ / r² for each charge.
- Account for direction: fields from both charges point in the same direction at midpoint.
- Add magnitudes.
Summary
- Draw clear diagrams and label knowns.
- Choose the correct equations before substituting numbers.
- Use symmetry and superposition principles.
- Check units and reasonableness of final answers.