Field of a Charged Rod - Revision history

Xcong6: /* Example 3: Using the Simulation to Analyze Field Strength (Numerical/Visual) */

2026-04-27T05:44:49Z

Example 3: Using the Simulation to Analyze Field Strength (Numerical/Visual)

← Older revision		Revision as of 01:44, 27 April 2026
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	* Point A: Directly above the midpoint of the rod		* Point A: Directly above the midpoint of the rod
			<div style="text-align: center;">[[File:Pos rod 1.png]]</div>

	* Point B: The same distance above one of the rod’s ends		* Point B: The same distance above one of the rod’s ends
			<div style="text-align: center;">[[File:Pos rod 2.png]]</div>


	'''Question:'''		'''Question:'''
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	'''Reflection:'''		'''Reflection:'''
	The field at Point A is stronger and points vertically due to symmetry. At Point B, the field is weaker and points diagonally inward toward the rod’s center. This shows the importance of symmetry in superposition, and helps illustrate “edge effects” that are harder to account for with algebra alone.		The field at Point A is stronger and points vertically due to symmetry. At Point B, the field is weaker and points diagonally inward toward the rod’s center. This shows the importance of symmetry in superposition, and helps illustrate “edge effects” that are harder to account for with algebra alone.


	=== Example 4: Using the Simulation to Analyze Field Strength 2 ===		=== Example 4: Using the Simulation to Analyze Field Strength 2 ===

Xcong6: added visual demonstration of example 1 and example 3 in the previous update. Added example 4 as a additional topic with a interactive model that allow students to see how the vector field and the observed charge changes in the different context.

2026-04-27T05:43:10Z

added visual demonstration of example 1 and example 3 in the previous update. Added example 4 as a additional topic with a interactive model that allow students to see how the vector field and the observed charge changes in the different context.

← Older revision		Revision as of 01:43, 27 April 2026
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	* Point A: Directly above the midpoint of the rod		* Point A: Directly above the midpoint of the rod
	~~<div style="text-align: center;">[[File:Pos rod 1.png]]</div>~~

	* Point B: The same distance above one of the rod’s ends		* Point B: The same distance above one of the rod’s ends
	~~<div style="text-align: center;">[[File:Pos rod 2.png]]</div>~~

	'''Question:'''		'''Question:'''
Line 196:		Line 193:
	'''Reflection:'''		'''Reflection:'''
	The field at Point A is stronger and points vertically due to symmetry. At Point B, the field is weaker and points diagonally inward toward the rod’s center. This shows the importance of symmetry in superposition, and helps illustrate “edge effects” that are harder to account for with algebra alone.		The field at Point A is stronger and points vertically due to symmetry. At Point B, the field is weaker and points diagonally inward toward the rod’s center. This shows the importance of symmetry in superposition, and helps illustrate “edge effects” that are harder to account for with algebra alone.


			=== Example 4: Using the Simulation to Analyze Field Strength 2 ===

			What happens when a rod is split into symmetrical half with opposite charges? Analyze the charge felt at different locations. Use the interactive diagram below for visual reference.

			[https://trinket.io/html/09b78c690248?showInstructions=true Interactive Charged Rod Simulation]


	== Connectedness ==		== Connectedness ==

Xcong6: /* Example 3: Using the Simulation to Analyze Field Strength (Numerical/Visual) */

2026-04-27T05:36:14Z

Example 3: Using the Simulation to Analyze Field Strength (Numerical/Visual)

← Older revision		Revision as of 01:36, 27 April 2026
Line 186:		Line 186:

	* Point A: Directly above the midpoint of the rod		* Point A: Directly above the midpoint of the rod
			<div style="text-align: center;">[[File:Pos rod 1.png]]</div>

	* Point B: The same distance above one of the rod’s ends		* Point B: The same distance above one of the rod’s ends
			<div style="text-align: center;">[[File:Pos rod 2.png]]</div>

	'''Question:'''		'''Question:'''
Line 193:		Line 196:
	'''Reflection:'''		'''Reflection:'''
	The field at Point A is stronger and points vertically due to symmetry. At Point B, the field is weaker and points diagonally inward toward the rod’s center. This shows the importance of symmetry in superposition, and helps illustrate “edge effects” that are harder to account for with algebra alone.		The field at Point A is stronger and points vertically due to symmetry. At Point B, the field is weaker and points diagonally inward toward the rod’s center. This shows the importance of symmetry in superposition, and helps illustrate “edge effects” that are harder to account for with algebra alone.


	== Connectedness ==		== Connectedness ==

Xcong6: minor coding error

2026-04-26T21:57:00Z

minor coding error

← Older revision		Revision as of 17:57, 26 April 2026
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	</math>		</math>

	<div style="text-align: center;">[[~~File:~~File:Rod charge step 3.png]]</div>		<div style="text-align: center;">[[File:Rod charge step 3.png]]</div>

Xcong6: the previous diagram has the rod and the observation point in the wrong coordinate. the new update fix this and adds a interactive model (accessed through Trinket html) that demonstrate the intergation process

2026-04-26T21:55:53Z

the previous diagram has the rod and the observation point in the wrong coordinate. the new update fix this and adds a interactive model (accessed through Trinket html) that demonstrate the intergation process

← Older revision		Revision as of 17:55, 26 April 2026
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	To calculate the electric field of a uniformly charged rod, we treat the rod as a continuous distribution of charge. Let the rod have total length <math>L</math> and total charge <math>Q</math>, centered along the x-axis. The observation point is located on the y-axis a distance <math>y</math> above the center.		To calculate the electric field of a uniformly charged rod, we treat the rod as a continuous distribution of charge. Let the rod have total length <math>L</math> and total charge <math>Q</math>, centered along the x-axis. The observation point is located on the y-axis a distance <math>y</math> above the center.

			Use the link below to access the interactive model!

			[https://trinket.io/html/c47edb36e316?showInstructions=true Interactive Electric Field Simulation]

	=== Step 1: Break the Rod into Pieces ===		=== Step 1: Break the Rod into Pieces ===
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	Each <math>dq</math> contributes a small electric field <math> d\vec{E} </math> at the observation point.		Each <math>dq</math> contributes a small electric field <math> d\vec{E} </math> at the observation point.

	~~[https://trinket.io/embed/html/c47edb36e316 Interactive Electric Field Simulation]~~		<div style="text-align: center;">[[File:Rod charge step 1.png]]</div>

	<div style="text-align: center;">[[File:~~ChargedRodBreakdown~~.png]]</div>

	=== Step 2: Write the Field Expression for One Piece ===		=== Step 2: Write the Field Expression for One Piece ===
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	</math>		</math>

	<div style="text-align: center;">[[File:~~ElectricFieldVectorFromRod~~.png]]</div>		<div style="text-align: center;">[[File:File:Rod charge step 3.png]]</div>

Xcong6: added, interactive model @ mathematical model step 1

2026-04-26T21:22:54Z

added, interactive model @ mathematical model step 1

← Older revision		Revision as of 17:22, 26 April 2026
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	Each <math>dq</math> contributes a small electric field <math> d\vec{E} </math> at the observation point.		Each <math>dq</math> contributes a small electric field <math> d\vec{E} </math> at the observation point.

			[https://trinket.io/embed/html/c47edb36e316 Interactive Electric Field Simulation]

	<div style="text-align: center;">[[File:ChargedRodBreakdown.png]]</div>		<div style="text-align: center;">[[File:ChargedRodBreakdown.png]]</div>

Xcong6 at 19:51, 26 April 2026

2026-04-26T19:51:43Z

← Older revision		Revision as of 15:51, 26 April 2026
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	'''~~Milo Karnes~~, Spring ~~2025~~'''		'''Xi Cong, Spring 2026'''

	== The Main Idea ==		== The Main Idea ==

Mkarnes3 at 21:05, 13 April 2025

2025-04-13T21:05:40Z

Show changes

Mkarnes3 at 20:49, 13 April 2025

2025-04-13T20:49:05Z

← Older revision		Revision as of 16:49, 13 April 2025
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	Each <math>dq</math> contributes a small electric field <math> d\vec{E} </math> at the observation point.		Each <math>dq</math> contributes a small electric field <math> d\vec{E} </math> at the observation point.

	[[~~Image~~:ChargedRodBreakdown.png~~\|600px\|center\|thumb\|Dividing the rod into segments, each producing a small electric field~~]]		<div style="text-align: center;">[[File:ChargedRodBreakdown.png]]</div>

	=== Step 2: Write the Field Expression for One Piece ===		=== Step 2: Write the Field Expression for One Piece ===
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	</math>		</math>

	[[~~Image~~:ElectricFieldVectorFromRod.png~~\|600px\|center\|thumb\|Vector from a rod element to the observation point~~]]		<div style="text-align: center;">[[File:ElectricFieldVectorFromRod.png]]</div>


	=== Step 4: Check the Result ===		=== Step 4: Check the Result ===

Mkarnes3 at 20:44, 13 April 2025

2025-04-13T20:44:32Z

Show changes