Electric Field & Potential Explorer
Map electric-field arrows, equipotential contours and a draggable probe for single, dipole and multi-charge arrangements.
NCERT alignment: Class 12; chapter Electric Charges and Fields. Exam practice: JEE Main, JEE Advanced, NEET.
Learning objectives
Students should use the live simulator to test a quantitative prediction, read measurements and explain the limits of the model. Do not rely on the animation alone: calculate the expected result before adjusting controls.
Theory, equations and interpretations
Coulomb field and scalar potential
A source point charge q creates a radial electric field and a scalar potential. Electric field is a vector, whereas potential is a scalar. For q in nC and distance in metres, kq/r has numeric factor 8.988q/r volts.
Important relation: E⃗ = kq r⃗/r³; V = kq/r
Superposition
For multiple stationary charges, add electric-field vectors component-wise, but add scalar potentials algebraically. A point with V=0 need not have E=0, as the midpoint of a dipole demonstrates.
Important relation: E⃗net = Σ E⃗ᵢ; Vnet = ΣVᵢ
Equipotential contours
An equipotential curve joins positions with the same V. Electrostatic E is perpendicular to each smooth equipotential curve because E = −∇V. Ideal point charges are excluded near the singularity.
Important relation: E⃗ = −∇V; ΔW = qΔV
Model scope
This is a static two-dimensional slice of a three-dimensional Coulomb field. It models charges in vacuum, no conductors, dielectric interfaces or time-varying electromagnetic fields.
Practical investigations
- Test a dipole midpoint: Place the probe at (0,0) for +q and −q charges. Predict V and explain why E remains non-zero.
- Like-charge symmetry: Set two positive charges and move the probe to the midpoint. Identify the balance of fields versus the nonzero positive potential.
- Distance law: Choose single charge; keep y=0 and double positive x (outside the excluded core). Determine how V and E scale.
- Draw a contour: Use the annotation tool to trace an equipotential and compare the tangent direction with the nearby field arrows.
Worked exam-style questions and answers
Q1. At the midpoint of an ideal electric dipole of equal opposite charges
Options: A. Both V and E are zero; B. V is zero but E is nonzero; C. E is zero but V is nonzero; D. Both are infinite
Answer: B. The scalar potentials cancel, while the electric-field vectors reinforce along the dipole axis.
Q2. The electric potential of a point charge falls with distance as
Options: A. 1/r; B. 1/r²; C. r; D. r²
Answer: A. For a point charge V=kq/r, choosing zero at infinity.
Q3. The electric field of a point charge falls with distance as
Options: A. r; B. 1/r; C. 1/r²; D. r²
Answer: C. Magnitude E=k|q|/r².
Q4. Electric field lines cross equipotential lines at
Options: A. 0°; B. 30°; C. 45°; D. 90°
Answer: D. E=−∇V, so field lines follow the normal to equipotential surfaces.
Q5. Which quantity must be added vectorially for a collection of charges?
Options: A. Potential; B. Electric field; C. Potential energy at fixed test charge; D. Charge magnitude
Answer: B. Electric field has both magnitude and direction.
Q6. At a location where V=0, electric field
Options: A. Must be zero; B. May be nonzero; C. Must be infinite; D. Does not exist
Answer: B. Potential zero does not generally imply its gradient is zero.
Common misconceptions and limitations
Ideal point charges have singular fields at their centres; probe readings inside a 0.13 m exclusion circle are deliberately undefined. Drawn contours are numerical approximations.
All learning content is available free of charge. The simulation is a simplified educational model. Check assumptions and units before applying a result. NANDAX SimStudio is not affiliated with NCERT or examination boards.
Teacher classroom use
Ask students to form a hypothesis, vary one parameter at a time, keep a record of graph readings, explain any change and compare results with the analytic relation. The on-screen worksheet offers questions with an answer key.