Potential Difference from Electric Field
For an electrostatic field, V_B-V_A=-integral_A^B E dot dl; path independence follows from curl E=0 in the region.
Why this shows up in the exam
parallel-plate regions · piecewise uniform fields · coordinate comparisons in a uniform field
Learn the idea
Potential change is the negative line integral of electric field. The field tells how rapidly electrical height falls. In a uniform field, only displacement along the field changes potential; sideways motion does not.
🧠 Memory hook: Move with E and V falls; move sideways and V stays.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- V_B-V_A = - integral_A^B E dot dl — electrostatic field
- Delta V = -E dot Delta r — uniform electric field
How to approach it
- 1Choose a path convenient for the field
- 2Evaluate E dot dl by region
- 3Check the sign from field direction
Common slip-ups that cost marks
- •Using total path length instead of projected displacement
- •Forgetting piecewise field changes
- •Using the uniform formula for varying E
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
Two point charges 1 microC and 2 microC are 1 m apart in vacuum. Take k = 9 x 10^9 SI. Find the force magnitude.
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