Circular Loop of Wire - Revision history

Rbeyersdorfer3 at 00:52, 6 December 2015

2015-12-06T00:52:12Z

← Older revision		Revision as of 20:52, 5 December 2015
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	<math>{\vec{B}_{net}}</math> = (0,0,-5.00e-5) T		<math>{\vec{B}_{net}}</math> = (0,0,-5.00e-5) T

			=Connectedness=
			By calculating the magnetic field of a loop, one can calculate the magnetic field and current of coils and solenoids. This has resonance in the mechanical engineering world, my major, in that engineers are constantly determining the fields of current through transformers, which are a series of coils, in order to properly account for the distribution electricity to an area. Without this knowledge of the magnetic field of a loop, engineers will not be able to redistribute electricity and current to various locations.
	=Resources=		=Resources=
	==Text==		==Text==
	''Matter and Interactions 4E, Chapter 19, Section 8.''		''Matter and Interactions 4E, Chapter 19, Section 8.''

Rbeyersdorfer3: /* Magnetic Field of a Loop */

2015-12-01T22:25:46Z

Magnetic Field of a Loop

← Older revision		Revision as of 18:25, 1 December 2015
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	====Magnetic Field of a Loop====		====Magnetic Field of a Loop====

	The formula to find the magnetic field of a loop is <math>{Δ\vec{B}_{loop}} = \frac{{µ}_{0}}{4π} * \frac{2πIR^2}{[R^2 + z^2]^{3/2}}</math>, where R is the radius of the loop, I is the conventional current throughout the loop , and z is the distance from the center of the loop along the axis.		The formula to find the magnetic field of a loop is <math>{\vec{B}_{loop}} = \frac{{µ}_{0}}{4π} * \frac{2πIR^2}{[R^2 + z^2]^{3/2}}</math>, where R is the radius of the loop, I is the conventional current throughout the loop , and z is the distance from the center of the loop along the axis.

	==Steps to Solving==		==Steps to Solving==

Rbeyersdorfer3: /* Middling */

2015-12-01T22:25:25Z

Middling

← Older revision		Revision as of 18:25, 1 December 2015
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	b.) Now that there are multiple turns of wire, the number of turns,N, must be multiplied to the <math>{\vec{B}_{loop}} </math> in order to account for the <math>{\vec{B}} </math> of the coil.		b.) Now that there are multiple turns of wire, the number of turns,N, must be multiplied to the <math>{\vec{B}_{loop}} </math> in order to account for the <math>{\vec{B}} </math> of the coil.
	<math>{\vec{B}_{coil}} = ~~<math>~~{\vec{B}_{loop}}*N </math>		<math>{\vec{B}_{coil}} = {\vec{B}_{loop}}*N </math>

	Plugging in known values:		Plugging in known values:

Rbeyersdorfer3: /* Middling */

2015-12-01T22:24:52Z

Middling

← Older revision		Revision as of 18:24, 1 December 2015
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	<math>{\vec{B}_{loop}} = 1.89 e-7 T </math>		<math>{\vec{B}_{loop}} = 1.89 e-7 T </math>

	b.) Now that there are multiple turns of wire, the number of turns,N, must be multiplied to the <math>{\vec{B}_{loop}}</math> in order to account for the <math>{\vec{B}} </math> of the coil.		b.) Now that there are multiple turns of wire, the number of turns,N, must be multiplied to the <math>{\vec{B}_{loop}} </math> in order to account for the <math>{\vec{B}} </math> of the coil.
	<math>{\vec{B}_{coil}} = <math>{\vec{B}_{loop}}*N </math>		<math>{\vec{B}_{coil}} = <math>{\vec{B}_{loop}}*N </math>

Rbeyersdorfer3: /* Middling */

2015-12-01T22:24:20Z

Middling

← Older revision		Revision as of 18:24, 1 December 2015
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	b.)Then, what would the magnitude of the magnetic field at the same location if there were 200 turns of wire in a coil instead of a loop?		b.)Then, what would the magnitude of the magnetic field at the same location if there were 200 turns of wire in a coil instead of a loop?

	a.) Since the observation location is at a distance .25 m from the center of the loop, the equation <math>{Δ\vec{B}_{loop}} = \frac{{µ}_{0}}{4π} * \frac{2πIR^2}{[R^2 + z^2]^{3/2}}</math>, will be used. R is the radius of the loop and z if the distance from the center of the loop.		a.) Since the observation location is at a distance .25 m from the center of the loop, the equation <math>{\vec{B}_{loop}} = \frac{{µ}_{0}}{4π} * \frac{2πIR^2}{[R^2 + z^2]^{3/2}}</math>, will be used. R is the radius of the loop and z if the distance from the center of the loop.

	Plugging in the known values, obtains:		Plugging in the known values, obtains:

	<math>{Δ\vec{B}_{loop}} = {1e-7} * \frac{2π(2A)(.05)^2}{[(.05)^2 + (.25)^2]^{3/2}}</math>		<math>{\vec{B}_{loop}} = {1e-7} * \frac{2π(2A)(.05)^2}{[(.05)^2 + (.25)^2]^{3/2}}</math>

	Solve:		Solve:

	<math>{Δ\vec{B}_{loop}} = 1.89 e-7 T </math>		<math>{\vec{B}_{loop}} = 1.89 e-7 T </math>

	b.) Now that there are multiple turns of wire, the number of turns,N, must be multiplied to the <math>{Δ\vec{B}_{loop}}</math> in order to account for the <math>{Δ\vec{B}} </math> of the coil.		b.) Now that there are multiple turns of wire, the number of turns,N, must be multiplied to the <math>{\vec{B}_{loop}}</math> in order to account for the <math>{\vec{B}} </math> of the coil.
	<math>{Δ\vec{B}_{coil}} = <math>{Δ\vec{B}_{loop}}*N </math>		<math>{\vec{B}_{coil}} = <math>{\vec{B}_{loop}}*N </math>

	Plugging in known values:		Plugging in known values:

	<math>{Δ\vec{B}_{coil}} = 1.89 e-7 T * 200 </math>		<math>{\vec{B}_{coil}} = 1.89 e-7 T * 200 </math>

	Solve:		Solve:

	<math>{Δ\vec{B}_{coil}} =3.78 e-5 T </math>		<math>{\vec{B}_{coil}} =3.78 e-5 T </math>

	===Difficult===		===Difficult===

Rbeyersdorfer3: /* Step 3 */

2015-12-01T22:22:49Z

Step 3

← Older revision		Revision as of 18:22, 1 December 2015
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	===Step 3===		===Step 3===
	The third step requires the summation of all the pieces of the loop and their contributions. This involves integrating over the circumference of the loop, which is 2. The integration is as follows:		The third step requires the summation of all the pieces of the loop and their contributions. This involves integrating over the circumference of the loop, which is 2π. The integration is as follows:
	<math>\int_0^{2π}\! {Δ\vec{B}_{z}} = \frac{{µ}_{0}}{4π} * \frac{IR^2Δθ}{[R^2 + z^2]^{3/2}}</math>		<math>\int_0^{2π}\! {Δ\vec{B}_{z}} = \frac{{µ}_{0}}{4π} * \frac{IR^2Δθ}{[R^2 + z^2]^{3/2}}</math>
	From here the formula for the magnetic field of a loop is derived (see Mathematical Model)		From here the formula for the magnetic field of a loop is derived (see Mathematical Model)

Rbeyersdorfer3: /* Magnetic Field of a Loop */

2015-12-01T22:22:01Z

Magnetic Field of a Loop

← Older revision		Revision as of 18:22, 1 December 2015
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	====Magnetic Field of a Loop====		====Magnetic Field of a Loop====

	The formula to find the magnetic field of a loop is <math>{Δ\vec{B}_{loop}} = \frac{{µ}_{0}}{4π} * \frac{2πIR^~~2Δθ~~}{[R^2 + z^2]^{3/2}}</math>, where R is the radius of the loop, I is the conventional current throughout the loop , and z is the distance from the center of the loop along the axis.		The formula to find the magnetic field of a loop is <math>{Δ\vec{B}_{loop}} = \frac{{µ}_{0}}{4π} * \frac{2πIR^2}{[R^2 + z^2]^{3/2}}</math>, where R is the radius of the loop, I is the conventional current throughout the loop , and z is the distance from the center of the loop along the axis.

	==Steps to Solving==		==Steps to Solving==

Rbeyersdorfer3: /* The Main Idea */

2015-12-01T22:20:19Z

The Main Idea

← Older revision		Revision as of 18:20, 1 December 2015
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	==The Main Idea==		==The Main Idea==

	This page is about calculating the magnetic field of a circular loop of wire. It uncovers the importance of this calculation as well as the formulas and examples associated with it.		This page is about calculating the magnetic field of a circular loop of wire. It uncovers the importance of this calculation as well as the formulas and examples associated with it. All information is derived from Matters and Interactions 4th Edition Textbook, chapter 19, section 8.

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

Rbeyersdorfer3: /* Difficult */

2015-12-01T22:19:09Z

Difficult

@@ Line 116: / Line 116: @@
 ===Difficult===
 =Resources=
 ==Text==
 ''Matter and Interactions 4E, Chapter 19, Section 8.''

Rbeyersdorfer3: /* Middling */

2015-12-01T22:04:26Z

Middling

← Older revision		Revision as of 18:04, 1 December 2015
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	===Middling===		===Middling===
			a.)A loop of wire carries a conventional current of 2 amperes. The radius of the loop is .05 m. Calculate the magnitude of the magnetic field at a distance .25 m from the center of the loop along the axis of the loop.
			b.)Then, what would the magnitude of the magnetic field at the same location if there were 200 turns of wire in a coil instead of a loop?

			a.) Since the observation location is at a distance .25 m from the center of the loop, the equation <math>{Δ\vec{B}_{loop}} = \frac{{µ}_{0}}{4π} * \frac{2πIR^2}{[R^2 + z^2]^{3/2}}</math>, will be used. R is the radius of the loop and z if the distance from the center of the loop.

			Plugging in the known values, obtains:

			<math>{Δ\vec{B}_{loop}} = {1e-7} * \frac{2π(2A)(.05)^2}{[(.05)^2 + (.25)^2]^{3/2}}</math>

			Solve:

			<math>{Δ\vec{B}_{loop}} = 1.89 e-7 T </math>

			b.) Now that there are multiple turns of wire, the number of turns,N, must be multiplied to the <math>{Δ\vec{B}_{loop}}</math> in order to account for the <math>{Δ\vec{B}} </math> of the coil.
			<math>{Δ\vec{B}_{coil}} = <math>{Δ\vec{B}_{loop}}*N </math>

			Plugging in known values:

			<math>{Δ\vec{B}_{coil}} = 1.89 e-7 T * 200 </math>

			Solve:

			<math>{Δ\vec{B}_{coil}} =3.78 e-5 T </math>

	===Difficult===		===Difficult===