Charged Disk - Revision history

Pnarala3 at 01:09, 26 April 2026

2026-04-26T01:09:39Z

← Older revision		Revision as of 21:09, 25 April 2026
Line 100:		Line 100:
	===Medium===		===Medium===

	A thin plastic disk, with its center at the origin and radius <math>0.60</math> m, is uniformly charged with charge <math>Q = 3.0 * 10^{-6} C</math>. What is the electric field of this disk at a location <math><0,0,0.20></math> m?		A thin plastic disk, with its center at the origin and radius <math>0.60</math> m, is uniformly charged with charge <math>Q = 3.0 \times 10^{-6} C</math>. What is the electric field of this disk at a location <math><0,0,0.20></math> m?

	<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">		<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
Line 108:		Line 108:
	Since <math>z = 0.20</math> m is not much smaller than <math>R = 0.60</math> m, we should use the full formula:		Since <math>z = 0.20</math> m is not much smaller than <math>R = 0.60</math> m, we should use the full formula:

	<math> E = \frac{1}{2\epsilon_0}\frac{Q}{\pi R^2}[1 - \frac{z}{(R^2+z^2)^{1/2}}]</math>		<math> E = \frac{1}{2\epsilon_0}\frac{Q}{\pi R^2}\left[1 - \frac{z}{(R^2 + z^2)^{1/2}}\right]</math>

	<math> E = \frac{1}{2\epsilon_0}\frac{3.0 * 10^{-6}}{\pi(0.60)^2}[1 - \frac{0.20}{((0.60)^2+(0.20)^2)^{1/2}}]</math>		<math> E = \frac{1}{2\epsilon_0}\frac{3.0 \times 10^{-6}}{\pi(0.60)^2}\left[1 - \frac{0.20}{((0.60)^2 + (0.20)^2)^{1/2}}\right]</math>

	<math> E = 1.04 * 10^5 \ N/C </math>		<math> E = 1.04 \times 10^5 \ N/C </math>

	Since the disk is positively charged, the electric field points in the positive z-direction.		Since the disk is positively charged, the electric field points in the positive z-direction.

Pnarala3 at 01:08, 26 April 2026

2026-04-26T01:08:05Z

← Older revision		Revision as of 21:08, 25 April 2026
Line 82:		Line 82:
	</div></div>		</div></div>

	===~~Middling~~===		===Medium===

	[[File:circle_3.png\|300px\|thumb\|Figure 3: Middling problem #2]]		[[File:circle_3.png\|300px\|thumb\|Figure 3: Middling problem #2]]
Line 98:		Line 98:
	</div></div>		</div></div>

	===~~Middling~~===		===Medium===

	A thin plastic disk, with its center at the origin and radius <math>0.60</math> m, is uniformly charged with charge <math>Q = 3.0 * 10^{-6} C</math>. What is the electric field of this disk at a location <math><0,0,0.20></math> m?		A thin plastic disk, with its center at the origin and radius <math>0.60</math> m, is uniformly charged with charge <math>Q = 3.0 * 10^{-6} C</math>. What is the electric field of this disk at a location <math><0,0,0.20></math> m?

Pnarala3 at 01:07, 26 April 2026

2026-04-26T01:07:49Z

← Older revision		Revision as of 21:07, 25 April 2026
Line 95:		Line 95:

	<math> \ E = \frac{4 * 10^{-7}}{2\epsilon_0π(0.4)^{2}} = 4.5 10^{4} N/C </math>		<math> \ E = \frac{4 * 10^{-7}}{2\epsilon_0π(0.4)^{2}} = 4.5 10^{4} N/C </math>

			</div></div>

			===Middling===

			A thin plastic disk, with its center at the origin and radius <math>0.60</math> m, is uniformly charged with charge <math>Q = 3.0 * 10^{-6} C</math>. What is the electric field of this disk at a location <math><0,0,0.20></math> m?

			<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
			<div style="font-weight:bold;line-height:1.6;">Solution</div>
			<div class="mw-collapsible-content">

			Since <math>z = 0.20</math> m is not much smaller than <math>R = 0.60</math> m, we should use the full formula:

			<math> E = \frac{1}{2\epsilon_0}\frac{Q}{\pi R^2}[1 - \frac{z}{(R^2+z^2)^{1/2}}]</math>

			<math> E = \frac{1}{2\epsilon_0}\frac{3.0 * 10^{-6}}{\pi(0.60)^2}[1 - \frac{0.20}{((0.60)^2+(0.20)^2)^{1/2}}]</math>

			<math> E = 1.04 * 10^5 \ N/C </math>

			Since the disk is positively charged, the electric field points in the positive z-direction.

	</div></div>		</div></div>

Pnarala3 at 01:04, 26 April 2026

2026-04-26T01:04:43Z

← Older revision		Revision as of 21:04, 25 April 2026
Line 57:		Line 57:

	Link to Computational Model: https://trinket.io/embed/glowscript/7298995b3d04		Link to Computational Model: https://trinket.io/embed/glowscript/7298995b3d04

			Users can drag around and zoom in and out to see different views of the model.

	The code sets up the charged disk as a flat circular surface made of many small cyan points. Each cyan point represents a small piece of charge on the disk. The program then uses superposition by calculating the electric field contribution from each small charge piece and adding those contributions together.		The code sets up the charged disk as a flat circular surface made of many small cyan points. Each cyan point represents a small piece of charge on the disk. The program then uses superposition by calculating the electric field contribution from each small charge piece and adding those contributions together.

Pnarala3 at 01:03, 26 April 2026

2026-04-26T01:03:12Z

← Older revision		Revision as of 21:03, 25 April 2026
Line 56:		Line 56:
	===A Computational Model===		===A Computational Model===

	~~The writers of the textbook Matter and Interactions 3rd Edition, have some great examples of VPython [http~~://~~www~~.~~phy.uct.ac.za~~/~~demonline~~/~~virtual~~/~~scripts/15_E_disk~~.~~py code] that~~ show, ~~in computational form,~~ the electric field ~~of a uniformly charged~~ disk. ~~To see~~ the ~~code in action~~, ~~take~~ a ~~look~~ at ~~[https://trinket~~.~~io/glowscript/3088e75439 this] or copy~~ the ~~code into your VIDLE shell~~. ~~Enjoy!~~		Link to Computational Model: https://trinket.io/embed/glowscript/7298995b3d04

			The code sets up the charged disk as a flat circular surface made of many small cyan points. Each cyan point represents a small piece of charge on the disk. The program then uses superposition by calculating the electric field contribution from each small charge piece and adding those contributions together.

			The yellow arrows are placed at fixed sample locations to show the general electric field pattern around the disk. The red points are movable observation points, and each red point has an orange arrow attached to it. These orange arrows show the electric field at those specific observation locations.

			The slider controls the z-distance from the disk. When the slider is moved, the red points shift to a new distance from the disk, and the code recalculates the electric field at each point. The orange arrows then update their direction and length, so the simulation shows both how the field points and how its strength changes with distance.

	~~[https://trinket.io/embed/glowscript/7298995b3d04]~~

	==Examples==		==Examples==

Pnarala3 at 00:59, 26 April 2026

2026-04-26T00:59:34Z

← Older revision		Revision as of 20:59, 25 April 2026
Line 58:		Line 58:
	The writers of the textbook Matter and Interactions 3rd Edition, have some great examples of VPython [http://www.phy.uct.ac.za/demonline/virtual/scripts/15_E_disk.py code] that show, in computational form, the electric field of a uniformly charged disk. To see the code in action, take a look at [https://trinket.io/glowscript/3088e75439 this] or copy the code into your VIDLE shell. Enjoy!		The writers of the textbook Matter and Interactions 3rd Edition, have some great examples of VPython [http://www.phy.uct.ac.za/demonline/virtual/scripts/15_E_disk.py code] that show, in computational form, the electric field of a uniformly charged disk. To see the code in action, take a look at [https://trinket.io/glowscript/3088e75439 this] or copy the code into your VIDLE shell. Enjoy!

	~~<html>~~		[https://trinket.io/embed/glowscript/7298995b3d04]
	~~<iframe src="~~https://trinket.io/embed/glowscript/7298995b3d04~~" width="900" height="750"></iframe>~~
	~~</html>~~

	==Examples==		==Examples==

Pnarala3 at 00:48, 26 April 2026

2026-04-26T00:48:10Z

← Older revision		Revision as of 20:48, 25 April 2026
Line 58:		Line 58:
	The writers of the textbook Matter and Interactions 3rd Edition, have some great examples of VPython [http://www.phy.uct.ac.za/demonline/virtual/scripts/15_E_disk.py code] that show, in computational form, the electric field of a uniformly charged disk. To see the code in action, take a look at [https://trinket.io/glowscript/3088e75439 this] or copy the code into your VIDLE shell. Enjoy!		The writers of the textbook Matter and Interactions 3rd Edition, have some great examples of VPython [http://www.phy.uct.ac.za/demonline/virtual/scripts/15_E_disk.py code] that show, in computational form, the electric field of a uniformly charged disk. To see the code in action, take a look at [https://trinket.io/glowscript/3088e75439 this] or copy the code into your VIDLE shell. Enjoy!

			<html>
	<iframe src="https://trinket.io/embed/glowscript/7298995b3d04" width="900" height="750"></iframe>		<iframe src="https://trinket.io/embed/glowscript/7298995b3d04" width="900" height="750"></iframe>
			</html>

	==Examples==		==Examples==

Pnarala3 at 00:46, 26 April 2026

2026-04-26T00:46:14Z

← Older revision		Revision as of 20:46, 25 April 2026
Line 58:		Line 58:
	The writers of the textbook Matter and Interactions 3rd Edition, have some great examples of VPython [http://www.phy.uct.ac.za/demonline/virtual/scripts/15_E_disk.py code] that show, in computational form, the electric field of a uniformly charged disk. To see the code in action, take a look at [https://trinket.io/glowscript/3088e75439 this] or copy the code into your VIDLE shell. Enjoy!		The writers of the textbook Matter and Interactions 3rd Edition, have some great examples of VPython [http://www.phy.uct.ac.za/demonline/virtual/scripts/15_E_disk.py code] that show, in computational form, the electric field of a uniformly charged disk. To see the code in action, take a look at [https://trinket.io/glowscript/3088e75439 this] or copy the code into your VIDLE shell. Enjoy!

	<iframe src="https://trinket.io/embed/glowscript/7298995b3d04" width="~~100%~~" height="~~356~~" ~~frameborder="0" marginwidth="0" marginheight="0" allowfullscreen~~></iframe>		<iframe src="https://trinket.io/embed/glowscript/7298995b3d04" width="900" height="750"></iframe>

	==Examples==		==Examples==

Pnarala3 at 00:45, 26 April 2026

2026-04-26T00:45:03Z

← Older revision		Revision as of 20:45, 25 April 2026
Line 58:		Line 58:
	The writers of the textbook Matter and Interactions 3rd Edition, have some great examples of VPython [http://www.phy.uct.ac.za/demonline/virtual/scripts/15_E_disk.py code] that show, in computational form, the electric field of a uniformly charged disk. To see the code in action, take a look at [https://trinket.io/glowscript/3088e75439 this] or copy the code into your VIDLE shell. Enjoy!		The writers of the textbook Matter and Interactions 3rd Edition, have some great examples of VPython [http://www.phy.uct.ac.za/demonline/virtual/scripts/15_E_disk.py code] that show, in computational form, the electric field of a uniformly charged disk. To see the code in action, take a look at [https://trinket.io/glowscript/3088e75439 this] or copy the code into your VIDLE shell. Enjoy!

	~~Also took a look at [~~https://~~phet~~.~~colorado.edu~~/en/~~simulation~~/~~legacy~~/~~capacitor-lab this] java applet for a lab simulation of a capacitor~~		<iframe src="https://trinket.io/embed/glowscript/7298995b3d04" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>

	==Examples==		==Examples==

Pnarala3 at 21:55, 25 April 2026

2026-04-25T21:55:01Z

← Older revision		Revision as of 17:55, 25 April 2026
Line 4:		Line 4:
	==The Main Idea==		==The Main Idea==

	The electric field of a charged disk can be ~~imagined~~ as the total electric field produced ~~from each point~~ on the disk. ~~We can relate this the~~ the Law of Superposition, ~~but considering~~ the disk as ~~a collection of~~ rings, ~~which will lead to a better understanding~~ of the electric ~~feild produced by~~ the ~~disk~~. This is especially ~~important because~~ two oppositely charged metal disks ~~collectively are known as~~ a ~~[[capacitor]], a concept seen in several places in physics and the real world~~.
			The electric field of a charged disk can be understood as the total electric field produced by all of the small pieces of charge on the disk. By using the Law of Superposition, we can treat the disk as many thin charged rings and add their electric field contributions together. Because the disk is symmetric, the sideways components of the electric field cancel along the central axis, leaving only a field in the z-direction. This idea is especially useful for understanding capacitors, since two oppositely charged metal disks or plates can create a nearly constant electric field between them.

	===A Mathematical Model===		===A Mathematical Model===