Uploaded June 2026 | Updated September 2026, 3 weeks ago
This animation demonstrates how Gauss’s law is used to determine the electric field produced by a long, uniformly charged line.
Starting from the symmetry of a continuous line of charge, we construct a cylindrical Gaussian surface and evaluate the electric flux through each part of that surface. The contribution from the end caps is shown to be zero, while the curved surface provides a direct path to solving for the electric field as a function of distance.
The derivation highlights:
• cylindrical symmetry and its implications
• the role of the Gaussian surface
• how electric flux simplifies using symmetry
• the relationship between linear charge density and electric field
The final result shows that the electric field decreases inversely with distance from the line:
E(r) = λ / (2π ε₀ r)
This video is designed for calculus-based introductory physics courses and emphasizes conceptual understanding alongside mathematical reasoning.
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Accessibility:
An alternative media version of this animation, including narration and full descriptive audio in readable form, is available for screen reader and eReader users. Link to the alternative media is in the YouTube card at the beginning of the video.
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Topics:
Gauss’s Law, electric flux, line charge, electric field, cylindrical symmetry, electromagnetism, physics derivation
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Ideal for:
• Introductory physics students (calculus-based)
• AP Physics / university E&M
• Review and concept reinforcement
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tags: Gauss law, Gauss's law derivation, line of charge, electric field line charge, linear charge density, electric flux, cylindrical symmetry, Gauss law example, electrostatics, electromagnetism, electric field derivation, Gaussian surface, physics tutorial, AP physics electricity, intro physics electromagnetism
This animation demonstrates how Gauss’s law is used to determine the electric field produced by a long, uniformly charged line.
Starting from the symmetry of a continuous line of charge, we construct a cylindrical Gaussian surface and evaluate the electric flux through each part of that surface. The contribution from the end caps is shown to be zero, while the curved surface provides a direct path to solving for the electric field as a function of distance.
The derivation highlights:
• cylindrical symmetry and its implications
• the role of the Gaussian surface
• how electric flux simplifies using symmetry
• the relationship between linear charge density and electric field
The final result shows that the electric field decreases inversely with distance from the line:
E(r) = λ / (2π ε₀ r)
This video is designed for calculus-based introductory physics courses and emphasizes conceptual understanding alongside mathematical reasoning.
---
Accessibility:
An alternative media version of this animation, including narration and full descriptive audio in readable form, is available for screen reader and eReader users. Link to the alternative media is in the YouTube card at the beginning of the video.
---
Topics:
Gauss’s Law, electric flux, line charge, electric field, cylindrical symmetry, electromagnetism, physics derivation
---
Ideal for:
• Introductory physics students (calculus-based)
• AP Physics / university E&M
• Review and concept reinforcement
---
tags: Gauss law, Gauss's law derivation, line of charge, electric field line charge, linear charge density, electric flux, cylindrical symmetry, Gauss law example, electrostatics, electromagnetism, electric field derivation, Gaussian surface, physics tutorial, AP physics electricity, intro physics electromagnetism
