Electric Field from Potential
For a differentiable electrostatic potential, E=-grad V; in one-dimensional or radial symmetry this reduces to the negative derivative along the varying coordinate.
Why this shows up in the exam
polynomial potential functions · field from V-versus-position graphs · charge density inferred through derivatives
Learn the idea
The electric field is the negative spatial slope of potential. A steep potential landscape produces a strong field; the minus sign says a positive test charge accelerates downhill in potential.
🧠 Memory hook: Field is minus the slope of V.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- E = -grad V — differentiable electrostatic potential
- E_r = -dV/dr — spherical or purely radial variation
How to approach it
- 1Identify the coordinate dependence
- 2Differentiate before substituting coordinates
- 3Check direction against decreasing V
Common slip-ups that cost marks
- •Dropping the minus sign
- •Differentiating with respect to the wrong coordinate
- •Treating a constant potential offset as a field
🌟 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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