Electric Field due to a Wire of finite length.

Summary

In this lecture, the derivation of electric field intensity due to a finite-length charged wire is presented. The speaker explains the geometry of the problem, the definition of electric field intensity, and the resolution of forces into components. By integrating these components over the length of the wire, the total electric field is calculated. A special case of an infinite-length wire is also discussed, demonstrating how its electric field can be derived using Gauss's Law, ultimately reinforcing the fundamental concepts of electrostatics.

Takeaways

• 📏 The lecture focuses on deriving the electric field intensity from a finite length wire.
• ⚡ The wire carries a uniform linear charge density, defined as λ (lambda) = Q/L.
• 📍 Point P is located at a perpendicular distance R from the wire, where the electric field intensity is calculated.
• 📐 The contribution to the electric field from a small segment dx is treated as a point charge.
• 🔍 The electric field intensity dE is calculated using Coulomb's law and resolved into x and y components.
• 🧮 Integration is used to find the total electric field intensity due to the entire length of the wire.
• 🔄 The integration accounts for the angles subtended by the wire's endpoints at point P.
• 💡 In the case of an infinite wire, both angles approach 90 degrees, simplifying calculations.
• 📊 The resulting electric field for an infinite wire is E = λ/(2πε₀R) along the x-axis.
• 🔗 The results obtained from this method match those derived using Gauss's law for both finite and infinite wires.

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