More Field Problems: UNIZOR.COM - Physics4Teens - Waves - Field Waves
Channel: Zor Shekhtman on UNIZOR Education
Date: 19/09/2022

UNIZOR.COM - Physics through a Looking Glass of Mathematician
Notes to a video lecture on http://www.unizor.com

More Field Problems

Problem 1
Prove that a curl of two-dimensional conservative vector field equals to zero.

Problem 2
Prove that a two-dimensional conservative field
F(x,y) = {P(x,y), Q(x,y)} = P(x,y)·i + Q(x,y)·j
is a gradient of some two-dimensional scalar field f(x,y) called its potential.
In other word, prove that there exists function f(x,y) such that
P(x,y) = ∂f(x,y)/∂x and 
Q(x,y) = ∂f(x,y)/∂y.

Problem 3
Prove that a curl of a gradient of a three-dimensional scalar field is zero.