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Magnetic field from two WiresLearning Goal: to understand exactly how to usage the rule of superposition in conjunction v the Biot-Savart (or Ampere"s) law.From the Biot-Savart law, it deserve to be calculated that the magnitude of the magnetic field because of a long straight cable is given by,where ( ) is the permeability constant, is the current in the wire, and also is the distance from the wire to the ar at i beg your pardon the magnitude of the magnetic field is gift calculated.

You are watching: Find the magnitude of the magnetic field b1k created at point k by wire 1.

The same an outcome can be acquired from Ampere"s law as well.

The direction of vector have the right to be uncovered using the right-hand rule. (Take care in applying the right-hand rule. Many students wrongly use your left hand while applying the right-hand rule due to the fact that those who use their right hand for creating sometimes automatically use their "pencil-free hand" to determine the direction the .)In this problem, you will be inquiry to calculate the magnetic field due to a collection of 2 wires with antiparallel currents as presented in the chart . Every of the wires dead a present of size . The existing in wire 1 is directed the end of the page and also that in cable 2 is directed into the page. The distance in between the wires is . The x axis is perpendicular come the line connecting the wires and also is equidistant from the wires.As girlfriend answer the questions posed here, try to look for a sample in her answers.Part AWhich of the vectors finest represents the direction that the magnetic field produced at point K (see the chart in the problem introduction) by cable 1 alone?Enter the variety of the vector with the proper direction.ANSWER: 3Correct

Part BWhich that the vectors finest represents the direction that the magnetic field created at allude K by wire 2 alone?Enter the variety of the vector with the suitable direction.ANSWER: 3Correct

Part CWhich of this vectors best represents the direction the the net magnetic field produced at point K by both wires?Enter the variety of the vector through the appropriate direction.ANSWER: 3Correct

Part DFind the size of the magnetic field created at point K by cable 1.Express her answer in regards to , , and appropriate constants.ANSWER: =Correct

Of course, because suggest K is equidistant indigenous the wires.Part EFind the magnitude of the network magnetic field created at allude K through both wires.Express her answer in terms of , , and also appropriate constants.ANSWER: =Correct

This result is relatively obvious due to the fact that of the the contrary of the problem: At allude K, the 2 wires each add equally come the magnetic field. In ~ points L and also M girlfriend should also consider the the contrary of the problem. However, it is in careful! The vectors will include up in a more facility way.Part FPoint together is located a street from the midpoint in between the 2 wires. Find the size of the magnetic field produced at allude L by cable 1.Hint F.1How to technique the problemHint not displayedExpress your answer in terms of , , and appropriate constants.ANSWER: =Correct

Part GPoint together is situated a street from the midpoint between the two wires. Find the magnitude of the net magnetic field produced at point L by both wires.Hint G.1How to technique the problemHint not displayedHint G.2Find the direction of the magnetic field as result of wire 1Hint no displayedHint G.3Find the direction the the magnetic field due to wire 2Hint no displayedHint G.4Find the direction of the network magnetic fieldHint no displayedHint G.5Angle in between magnetic field as result of wire 1 and the x axisHint not displayedHint G.6Find the angle in between magnetic field because of wire 1 and also the x axisHint not displayedHint G.7Net magnetic fieldHint no displayedExpress your answer in regards to , , and appropriate constants.ANSWER: =Correct

Part HPoint M is situated a street from the midpoint in between the 2 wires. Uncover the magnitude of the magnetic field developed at suggest M by cable 1.Express her answer in regards to , , and appropriate constants.ANSWER: =Correct

Part IFind the magnitude of the network magnetic field produced at suggest M by both wires.Hint I.1How to strategy the problemHint no displayedHint I.2Find the direction that the magnetic field due to wire 1Hint no displayedHint I.3Find the direction that the network magnetic fieldHint not displayedHint I.4Angle in between magnetic field due to wire 1 and the x axisHint not displayedHint I.5Find the angle between magnetic field because of wire 1 and also the x axisHint no displayedHint I.6Net magnetic fieldHint no displayedExpress her answer in regards to , , and also appropriate constants.ANSWER: =Correct

Part JFinally, consider point X (not displayed in the diagram) located on the x axis an extremely far away in the optimistic x direction. I beg your pardon of the vectors best represents the direction the the magnetic field produced at allude X by wire 1 alone?Enter the variety of the vector with the proper direction.ANSWER: Answer not displayed

Part KWhich of the vectors ideal represents the direction of the magnetic field created at point X by cable 2 alone?Enter the number of the vector with the appropriate direction.ANSWER: Answer no displayed

Problem 33.8Part AWhat existing is necessary to create the magnetic field strength of in ~ a suggest 2.3 from a long, directly wire?Express your answer using two significant figures.ANSWER: =5.8Correct

Part BWhat present is required to create the magnetic field strength of in ~ a suggest 2.3 from a long, straight wire?Express your answer making use of two far-ranging figures.ANSWER: =580Correct

Part CWhat existing is necessary to generate the magnetic ar strength of at a allude 2.3 native a long, directly wire?Express your answer making use of two far-reaching figures.ANSWER: =Answer not presented

Part DWhat current is required to create the magnetic field strength of at a suggest 2.3 indigenous a long, straight wire?Express your answer making use of two far-reaching figures.ANSWER: =Answer no displayed

Magnetic ar from 2 WiresLearning Goal: come understand just how to use the rule of superposition in conjunction v the Biot-Savart (or Ampere"s) law.From the Biot-Savart law, it have the right to be calculated that the magnitude of the magnetic field because of a lengthy straight cable is given by,where ( ) is the permeability constant, is the current in the wire, and is the street from the wire to the place at which the size of the magnetic field is being calculated.

The same an outcome can be obtained from Ampere"s law as well.

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The direction that vector can be found using the right-hand rule. (Take care in using the right-hand rule. Countless students mistakenly use their left hand while using the right-hand rule because those who use their right hand for composing sometimes instantly use their "pencil-free hand" to recognize the direction the .)In this problem, you will certainly be request to calculation the magnetic field as result of a set of 2 wires through antiparallel currents as shown in the chart . Each of the wires tote a current of magnitude . The existing in wire 1 is directed out of the page and that in wire 2 is directed into the page. The distance in between the wires is . The x axis is perpendicular to the line connecting the wires and also is equidistant native the wires.As friend answer the concerns posed here, try to look because that a sample in your answers.Part AWhich that the vectors finest represents the direction that the magnetic field produced at point K (see the diagram in the trouble introduction) ...