Forest UCM Energy CurlFcons - Revision history

Foretony: /* Aside on uniform electric field */

2021-09-23T22:00:51Z

Aside on uniform electric field

2021-09-23T21:59:20Z

A test for path independence of a force

2014-09-24T12:38:53Z

Force that depends on r

2014-09-24T12:36:54Z

Aside on uniform electric field

2014-09-24T12:36:41Z

Aside on uniform electric field

2014-09-24T12:32:59Z

Aside on uniform electric field

2014-09-24T12:15:23Z

Aside on uniform electric field

2014-09-24T12:14:12Z

Aside on uniform electric field

2014-09-24T12:13:59Z

Force that depends on r

2014-09-24T12:10:41Z

Force that depends on r

← Older revision		Revision as of 22:00, 23 September 2021
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	and we can use the coulomb force argument to show that the force is conservative.		and we can use the coulomb force argument to show that the force is conservative.

−	If you construct a capacitor with a uniform electric field between its plates, the Force is constant as a result of the summation of all the Forces between individual charges but the fundamental force responsible for the uniform electric field is itself a function of ~~posiiton~~.	+	If you construct a capacitor with a uniform electric field between its plates, the Force is constant as a result of the summation of all the Forces between individual charges but the fundamental force responsible for the uniform electric field is itself a function of position.

@@ Line 70: / Line 70: @@
 :<math> \vec \nabla \times \vec F=0</math>
-Then <math>\vec F</math> is a cosnervative force
+Then <math>\vec F</math> is a conservative force
 or if you are given a potential for the force such that

← Older revision		Revision as of 12:38, 24 September 2014
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	:<math>\vec \nabla \times \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^3} \vec r =0</math>		:<math>\vec \nabla \times \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^3} \vec r =0</math>
		+
		+
		+	===The potential===
		+
		+	The potential energy for this force may be defined according to the work integral
		+
		+	:<math>U(r) = - W = - \int \vec F \cdot d \vec r</math>

	==Aside on uniform electric field==		==Aside on uniform electric field==

@@ Line 132: / Line 132: @@
 Maxwells equations have
-:<math>\vec \nabla E = - \frac{\partial \vec B}{\partial t}</math>
+:<math>\vec \nabla \times \vec E = - \frac{\partial \vec B}{\partial t}</math>
 If the magnetic field is not time dependent then you clearly have a curl of zero for the force (electrostatics)

← Older revision		Revision as of 12:36, 24 September 2014
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		+
		+	also
		+
		+	Maxwells equations have
		+
		+	:<math>\vec \nabla E = - \frac{\partial \vec B}{\partial t}</math>
		+
		+	If the magnetic field is not time dependent then you clearly have a curl of zero for the force (electrostatics)


	[[Forest_UCM_Energy#Second_requirement_for_Conservative_Force]]		[[Forest_UCM_Energy#Second_requirement_for_Conservative_Force]]

← Older revision		Revision as of 12:32, 24 September 2014
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	and we can use the coulomb force argument to show that the force is conservative.		and we can use the coulomb force argument to show that the force is conservative.
		+
		+	If you construct a capacitor with a uniform electric field between its plates, the Force is constant as a result of the summation of all the Forces between individual charges but the fundamental force responsible for the uniform electric field is itself a function of posiiton.

← Older revision		Revision as of 12:15, 24 September 2014
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	:<math>\vec E = \frac{1}{4 \pi \epsilon_0} \frac{ q_2}{r^3} \vec r \equiv \frac{C}{r^3} \vec r</math>		:<math>\vec E = \frac{1}{4 \pi \epsilon_0} \frac{ q_2}{r^3} \vec r \equiv \frac{C}{r^3} \vec r</math>
		+
		+	and we can use the coulomb force argument to show that the force is conservative.

@@ Line 116: / Line 116: @@
 The first part of the Lorentz force indicates that
-:\vec F = q \vec E
+:<math>\vec F = q \vec E</math>
 if q is near a point charge then

← Older revision		Revision as of 12:13, 24 September 2014
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	:<math>\vec \nabla \times \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^3} \vec r =0</math>		:<math>\vec \nabla \times \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^3} \vec r =0</math>
		+
		+	==Aside on uniform electric field==
		+
		+	The first part of the Lorentz force indicates that
		+
		+	:\vec F = q \vec E
		+
		+	if q is near a point charge then
		+
		+	:<math>\vec E = \frac{1}{4 \pi \epsilon_0} \frac{ q_2}{r^3} \vec r \equiv \frac{C}{r^3} \vec r</math>
		+
		+


	[[Forest_UCM_Energy#Second_requirement_for_Conservative_Force]]		[[Forest_UCM_Energy#Second_requirement_for_Conservative_Force]]

← Older revision		Revision as of 12:10, 24 September 2014
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	</math>		</math>

−	: <math>\left . \left ( \vec \nabla \times \vec F \right ) \right \|_x = -3C \left ( -\frac{3y}{r^5} z- -\frac{z}{r^5} y\right ) =0 </math>	+	: <math>\left . \left ( \vec \nabla \times \vec F \right ) \right \|_x = -3C \left ( -\frac{y}{r^5} z- -\frac{z}{r^5} y\right ) =0 </math>