Conservative Force Field & Scalar Potential Function | VTU 1BMATE201 Model Paper Q3(b)

📘 VTU Model Question Paper – 2025 (Question Paper Information)

Course: 1BMATE201 – Calculus, Laplace Transforms and Numerical Techniques
Paper: Model Question Paper–I (2025 Scheme)
Question No.: 3(b)

Question:

Show that

F⃗ = (2xy² + yz) i⃗ + (2x²y + xz + 2yz²) j⃗ + (2y²z + xy) k⃗

is a conservative force field (Irrotational).

Find its scalar function ϕ such that

F⃗ = ∇ϕ.

In this video, we solve an important VTU Model Question Paper problem from Vector Calculus. The solution is explained step by step by verifying that the given vector field is irrotational using curl, and then determining the scalar potential function ϕ such that F⃗ = ∇ϕ.

🎯 Topics Covered:
✅ Vector Calculus
✅ Conservative Vector Fields
✅ Irrotational Vector Fields
✅ Curl of a Vector Field
✅ Scalar Potential Function
✅ Gradient Operator
✅ VTU Model Question Paper 2025
✅ Engineering Mathematics-II

📌 Watch Next:

Module 2 Vector Calculus Playlist:
https://www.youtube.com/

📚 Related Topics:
• Gradient
• Divergence
• Curl
• Conservative Vector Fields
• Scalar Potential Function
• Line Integrals
• Green’s Theorem
• Stokes’ Theorem
• Gauss Divergence Theorem

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