Electromagnetism
Line charge field
The line charge creates a cylindrically symmetric field; test the E arrows above and below the line.
Line charge field — interactive Electromagnetism simulation. The line charge creates a cylindrically symmetric field; test the E arrows above and below the line. Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Line charge field
The line charge creates a cylindrically symmetric field; test the E arrows above and below the line.
A uniform line charge λ produces a cylindrically symmetric electric field E ∝ λ/r perpendicular to the line. A static line charge has no current, so B = 0 — only the electric force F_E = qE acts on a test charge (shown as the yellow F_E arrow). Compare |E| above and below the line in the Properties panel; halving the distance doubles the field.
- E ∝ λ/r (cylindrical)
- F = qE
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
A finite straight rod carries charge spread uniformly along its length. On the perpendicular bisector, does the field from a line of charge follow the same 1/r² law as a point charge?
Predictions to weigh
- Yes — from far enough away, it still looks like a point charge.
- The field doesn't depend on distance from an extended charge distribution.
- No — a finite line of charge has its own, more complex distance dependence, not a simple 1/r² law.
Variable roles
What you set:
- Perpendicular distance d (m)
What you measure:
- Field strength E_y (N/C)
How the investigation runs
- Open the line-charge preset and press Reset. The rod carries a linear charge density of 2 nC/m over a 4.8 m length.
- Enable the field-strength readout on the perpendicular bisector.
- Set the perpendicular distance from the rod's midpoint for each trial and record the field strength.
Governing equation
Field of a Finite Charged Line (on the Bisector) — E = k·q/r²
Integrating Coulomb's law along a uniformly charged rod gives a field on the perpendicular bisector that interpolates between an infinite line's 1/d falloff (close up) and a point charge's 1/d² falloff (far away).
What the printable worksheet asks students to work out
- For one trial, compute E_y = −2kλL_half/(d·√(L_half² + d²)) using k = 8.99×10⁹ N·m²/C², λ = 2 nC/m, L_half = 2.4 m. Compare to the table.
- Explain why a finite line of charge's field doesn't reduce to a clean power law like 1/r² — it depends on both the distance d and the rod's half-length through the combination √(L_half² + d²).
Where this shows up beyond the lab
- As distance d gets very small compared to the rod's length, the formula approaches E ≈ −2kλ/d (the classic 'infinite line of charge' result, which drops as 1/d not 1/d²). Explain, using your formula, why the finite rod behaves like an infinite one when you're close to it.
- As distance d gets very large compared to the rod's length, the formula should approach the point-charge result E ≈ kQ_total/d² (with Q_total = λ·2L_half). Explain physically why an extended charge distribution looks like a point charge from far enough away.
- AP Physics 2 — Unit 10: Electric Force, Field, and Potential
- AP Physics C: Electricity and Magnetism — Unit 8: Electric Charges, Fields, and Gauss's Law
- IB Physics — D.2 Electric and magnetic fields
- General High School Physics — Magnetism & electromagnetism
- NGSS High School Physics — Gravitational and electrostatic forces
- Welcome to Line Charge
- Select the test charge
- Press Play
- Field of a line charge
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.