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Tagged with vector-fieldsforces
47 questions
1vote
1answer
134views
Minimizing the absolute value of a line integral over a non-conservative vector field
I have heard the comparison between line integrals and work, so how would I minimize the absolute value of the line integral of two points over a non-conservative vector field (if it were conservative,...
1vote
1answer
140views
Exact test for checking conservative forces
What is the nature of this force on the path $x^2+y^2=1$? $$\tag1\vec F=\frac{-y\,\hat{i }+x\,\hat{j}}{x^2+y^2}.$$ I tried two methods, but they give different answers: For this specific path it ...
- 113
10votes
5answers
2kviews
Intuition for vector calculus identities
I can follow the proofs for these identities, but I struggle to intuitively understand why they must be true: $$$$ 1. The curl of a gradient of a twice-differentiable scalar field is zero: $$\nabla\...
- 148
3votes
3answers
2kviews
Why is the work done non-zero even though it's along a closed path?
So, in this problem I just solved there is a force field given by $\mathbf{F} = -x \hat{\mathbf{j}}$ and I need to compute the work done on a particle along a circular path of radius $R$, centred at ...
- 33
0votes
1answer
71views
How do force-fields (i.e. electric field) apply "force at a distance"?
I often see when an article or text describes a "field of force" (for this question lets use the electric field) that they say that its a "forces at a distance". Whats going on ...
- 113
2votes
1answer
228views
What is the vector field associated with potential energy?
The mere concept of a line integral is defined for a vector field, and I thus thought the following was a rigorous and general definition of potential energy: Definition: Given a conservative force ...
- 379
-1votes
1answer
48views
Conservation and potential with non-cartesian forces
I understand how to determine if a force is conservative from \begin{equation} \nabla\times \mathbf{F}=0 \implies \mathbf{F}\text{ is conservative} \end{equation} When $F$ is in cartesian coordinates. ...
- 19
0votes
1answer
681views
Gravitational field strength between equipotential lines
Is the gravitational field strength between two equipotential lines the same at all distances? For example, in the image, does point P experience the same gravitational field strength as a point ...
0votes
2answers
823views
Intuition behind a line integral over a vector field
I have seen answers to this question on this site already, though I still do not understand what line integrals and there results represent and would appreciate an oversimplified description. I have ...
0votes
0answers
87views
Find the curl if the vector field depends on a parameter
Given the following vector, \begin{align} F(x(t),y(t),z(t)) &= \begin{bmatrix} \omega_1^2 x_o\cos(\omega_1 t) \\ \omega_2y_0\sin(\omega_2 t)\\ 0\\ \...
- 173
0votes
1answer
78views
Can anyone tell me how does conservative forces work? Confused
From vector calculus, I'd learnt that a conservative vector field satisfies $$ \textbf{F} = \boldsymbol{\nabla} g $$ which $\textbf{F}$ is the gradient of some scalar-valued function, and $g$ is the ...
1vote
4answers
662views
Why isn't the magnetic field defined by the magnetic force on a particle moving through it?
A magnetic field describes the influence a charge (in motion) experiences. In other words, it is essentially a vector field that describes the force that a particle will feel at a given location. ...
2votes
3answers
767views
Why can a force field only be conservative if it is spherically symmetric?
I saw in my textbook that a field can only be conservative if it happens to be spherically symmetric. Why is this so? Is there a good proof for this?
user274567
1vote
1answer
442views
The curl of a friction force being zero
Consider the resistive force modelled by the function $\vec{F} = -b\vec{v}(t)$. The curl of this function, $\nabla \times \vec{F}$, is $$[\frac{\partial}{\partial y} (\frac{dz}{dt}) - \frac{\partial}{\...
- 485
0votes
2answers
403views
Force through potential energy: does the absolute value of energy has sense?
Force can be found from potential energy: $$\vec{F}=-\nabla U$$ In other words, force depends on how the potential energy changes in space, but not on the potential energy value? Or if we take ...
