Magnetic Field of a Long Straight Wire - Revision history

Gcarneiro6: /* Models */

2026-04-25T21:12:56Z

Models

@@ Line 59: / Line 59: @@
 ::<math>B = \frac{\mu_0}{4\pi} \frac{IL}{z\sqrt{z^2 + (L/2)^2}}</math>
 ====Approximation====
@@ Line 86: / Line 126: @@
 	•	But 2× more segments are contributing (the ×r part)
 Net result: the field is only 2× weaker, not 4×. That is exactly 1/r behavior.
 == Superposition Principle ==

Gcarneiro6: /* Superposition Principle */

2026-04-25T21:08:14Z

Superposition Principle

← Older revision		Revision as of 17:08, 25 April 2026
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	Mathematically:		Mathematically:

	::\mathbf{B~~}_{\text{total}~~} = \mathbf{B}_1 + \mathbf{B}_2 + \mathbf{B}_3 + \cdots		::<math> d\mathbf{B} = \mathbf{B}_1 + \mathbf{B}_2 + \mathbf{B}_3 + \cdots </math>


	===How to Apply Superposition===		===How to Apply Superposition===

Gcarneiro6: /* Important Notes */

2026-04-25T21:04:11Z

Important Notes

← Older revision		Revision as of 17:04, 25 April 2026
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	===Important Notes===		===Important Notes===

	* Magnetic fields are ~~‘’‘vectors’’’~~, so direction matters.		* Magnetic fields are vectors, so direction matters.
	* Fields can ~~‘’‘cancel out’’’~~ if they point in opposite directions.		* Fields can cancel out if they point in opposite directions.
	* Fields can ~~‘’‘reinforce~~ each ~~other’’’~~ if they point in the same direction.		* Fields can reinforce each other if they point in the same direction.
	* In many problems, symmetry can simplify the vector addition.		* In many problems, symmetry can simplify the vector addition.

Gcarneiro6: /* How to Apply Superposition */

2026-04-25T21:03:44Z

How to Apply Superposition

← Older revision		Revision as of 17:03, 25 April 2026
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	To correctly find the total magnetic field:		To correctly find the total magnetic field:

	~~‘’‘Find~~ the magnetic field from each wire ~~individually’’’~~		1) Find the magnetic field from each wire individually

	~~‘’‘Determine~~ the direction of each field’’’ using the right-hand rule		2) Determine the direction of each field’’’ using the right-hand rule

	~~‘’‘Add~~ the fields as ~~vectors’’’~~ (not just magnitudes)		3)Add the fields as vectors (not just magnitudes)

	===Important Notes===		===Important Notes===

Gcarneiro6 at 21:02, 25 April 2026

2026-04-25T21:02:53Z

@@ Line 86: / Line 86: @@
 	•	But 2× more segments are contributing (the ×r part)
 Net result: the field is only 2× weaker, not 4×. That is exactly 1/r behavior.
 ==GlowScript Code Example: Wire Interaction==

Gcarneiro6: /* Common Mistake */

2026-04-25T21:01:14Z

Common Mistake

← Older revision		Revision as of 17:01, 25 April 2026
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	* Using the long-wire formula when it is not valid:		* Using the long-wire formula when it is not valid:
	The formula below only applies when the wire is much longer than the distance. Otherwise, the full Biot–Savart result must be used.		The formula below only applies when the wire is much longer than the distance. Otherwise, the full Biot–Savart result must be used.
	:::<math>B = \frac{\mu_{0}}{4\pi}\frac{2I}{r}</math>		:::<math>B = \frac{\mu_{0}}{4\pi}\frac{2I}{r}</math>
	* Confusing magnetic field direction with force direction:		* Confusing magnetic field direction with force direction:
	The magnetic field direction is NOT the same as the force on a charge or another wire. Forces require an additional rule.		The magnetic field direction is NOT the same as the force on a charge or another wire. Forces require an additional rule.

Gcarneiro6: /* Common Mistake */

2026-04-25T21:01:04Z

Common Mistake

← Older revision		Revision as of 17:01, 25 April 2026
Line 280:		Line 280:
	The magnetic field does NOT point outward from the wire. It forms concentric circles around the wire.		The magnetic field does NOT point outward from the wire. It forms concentric circles around the wire.
	* Using the long-wire formula when it is not valid:		* Using the long-wire formula when it is not valid:
	The formula :::<math>B = \frac{\mu_{0}}{4\pi}\frac{2I}{r}</math> ~~only applies when the wire is much longer than the distance . Otherwise, the full Biot–Savart result must be used.~~		The formula below only applies when the wire is much longer than the distance. Otherwise, the full Biot–Savart result must be used.
			:::<math>B = \frac{\mu_{0}}{4\pi}\frac{2I}{r}</math>
	* Confusing magnetic field direction with force direction:		* Confusing magnetic field direction with force direction:
	The magnetic field direction is NOT the same as the force on a charge or another wire. Forces require an additional rule.		The magnetic field direction is NOT the same as the force on a charge or another wire. Forces require an additional rule.

Gcarneiro6: /* Common Mistake */

2026-04-25T21:00:23Z

Common Mistake

← Older revision		Revision as of 17:00, 25 April 2026
Line 280:		Line 280:
	The magnetic field does NOT point outward from the wire. It forms concentric circles around the wire.		The magnetic field does NOT point outward from the wire. It forms concentric circles around the wire.
	* Using the long-wire formula when it is not valid:		* Using the long-wire formula when it is not valid:
	The formula		The formula :::<math>B = \frac{\mu_{0}}{4\pi}\frac{2I}{r}</math> only applies when the wire is much longer than the distance . Otherwise, the full Biot–Savart result must be used.
	:::<math>B = \frac{\mu_{0}}{4\pi}\frac{2I}{r}</math> only applies when the wire is much longer than the distance . Otherwise, the full Biot–Savart result must be used.
	* Confusing magnetic field direction with force direction:		* Confusing magnetic field direction with force direction:
	The magnetic field direction is NOT the same as the force on a charge or another wire. Forces require an additional rule.		The magnetic field direction is NOT the same as the force on a charge or another wire. Forces require an additional rule.

Gcarneiro6: /* Common Mistake */

2026-04-25T21:00:07Z

Common Mistake

← Older revision		Revision as of 17:00, 25 April 2026
Line 280:		Line 280:
	The magnetic field does NOT point outward from the wire. It forms concentric circles around the wire.		The magnetic field does NOT point outward from the wire. It forms concentric circles around the wire.
	* Using the long-wire formula when it is not valid:		* Using the long-wire formula when it is not valid:
	The formula ::<math>~~d\mathbf{~~B} = \frac{\~~mu_0 I~~}{2\pi r} only applies when the wire is much longer than the distance . Otherwise, the full Biot–Savart result must be used.		The formula
			:::<math>B = \frac{\mu_{0}}{4\pi}\frac{2I}{r}</math> only applies when the wire is much longer than the distance . Otherwise, the full Biot–Savart result must be used.
	* Confusing magnetic field direction with force direction:		* Confusing magnetic field direction with force direction:
	The magnetic field direction is NOT the same as the force on a charge or another wire. Forces require an additional rule.		The magnetic field direction is NOT the same as the force on a charge or another wire. Forces require an additional rule.

Gcarneiro6: /* Common Mistake */

2026-04-25T20:58:41Z

Common Mistake

← Older revision		Revision as of 16:58, 25 April 2026
Line 280:		Line 280:
	The magnetic field does NOT point outward from the wire. It forms concentric circles around the wire.		The magnetic field does NOT point outward from the wire. It forms concentric circles around the wire.
	* Using the long-wire formula when it is not valid:		* Using the long-wire formula when it is not valid:
	The formula ::<math>d\mathbf{B}=\frac{\mu_0 I}{2\pi r} only applies when the wire is much longer than the distance . Otherwise, the full Biot–Savart result must be used.		The formula ::<math>d\mathbf{B} = \frac{\mu_0 I}{2\pi r} only applies when the wire is much longer than the distance . Otherwise, the full Biot–Savart result must be used.
	* Confusing magnetic field direction with force direction:		* Confusing magnetic field direction with force direction:
	The magnetic field direction is NOT the same as the force on a charge or another wire. Forces require an additional rule.		The magnetic field direction is NOT the same as the force on a charge or another wire. Forces require an additional rule.