# Physics: Current, Magnetic Field, Vector, and Biot-Savart Law

Magnetic Field from Two Wires

Learning Goal: To understand how to use the principle of superposition in conjunction with the Biot-Savart (or Ampere's) law.

From the Biot-Savart law, it can be calculated that the magnitude of the magnetic field due to a long straight wire is given by

,

where ( ) is the permeability constant, is the current in the wire, and is the distance from the wire to the location at which the magnitude of the magnetic field is being calculated.

The same result can be obtained from Ampere's law as well.

The direction of vector can be found using the right-hand rule. (Take care in applying the right-hand rule. Many students mistakenly use their left hand while applying the right-hand rule since those who use their right hand for writing sometimes automatically use their "pencil-free hand" to determine the direction of .)

In this problem, you will be asked to calculate the magnetic field due to a set of two wires with antiparallel currents as shown in the diagram . Each of the wires carries a current of magnitude . The current in wire 1 is directed out of the page and that in wire 2 is directed into the page. The distance between the wires is . The x axis is perpendicular to the line connecting the wires and is equidistant from the wires.

As you answer the questions posed here, try to look for a pattern in your answers.

Part A

Which of the vectors best represents the direction of the magnetic field created at point K (see the diagram in the problem introduction) by wire 1 alone?

Enter the number of the vector with the appropriate direction.

ANSWER: 3

Correct

Part B

Which of the vectors best represents the direction of the magnetic field created at point K by wire 2 alone?

Enter the number of the vector with the appropriate direction.

ANSWER: 3

Correct

Part C

Which of these vectors best represents the direction of the net magnetic field created at point K by both wires?

Enter the number of the vector with the appropriate direction.

ANSWER: 3

Correct

Part D

Find the magnitude of the magnetic field created at point K by wire 1.

Express your answer in terms of , , and appropriate constants.

ANSWER: =

Correct

Of course, because point K is equidistant from the wires.

Part E

Find the magnitude of the net magnetic field created at point K by both wires.

Express your answer in terms of , , and appropriate constants.

ANSWER: =

Correct

This result is fairly obvious because of the symmetry of the problem: At point K, the two wires each contribute equally to the magnetic field. At points L and M you should also consider the symmetry of the problem. However, be careful! The vectors will add up in a more complex way.

Part F

Point L is located a distance from the midpoint between the two wires. Find the magnitude of the magnetic field created at point L by wire 1.

Hint F.1 How to approach the problem

Hint not displayed

Express your answer in terms of , , and appropriate constants.

ANSWER: =

Correct

Part G

Point L is located a distance from the midpoint between the two wires. Find the magnitude of the net magnetic field created at point L by both wires.

Hint G.1 How to approach the problem

Hint not displayed

Hint G.2 Find the direction of the magnetic field due to wire 1

Hint not displayed

Hint G.3 Find the direction of the magnetic field due to wire 2

Hint not displayed

Hint G.4 Find the direction of the net magnetic field

Hint not displayed

Hint G.5 Angle between magnetic field due to wire 1 and the x axis

Hint not displayed

Hint G.6 Find the angle between magnetic field due to wire 1 and the x axis

Hint not displayed

Hint G.7 Net magnetic field

Hint not displayed

Express your answer in terms of , , and appropriate constants.

ANSWER: =

Correct

Part H

Point M is located a distance from the midpoint between the two wires. Find the magnitude of the magnetic field created at point M by wire 1.

Express your answer in terms of , , and appropriate constants.

ANSWER: =

Correct

Part I

Find the magnitude of the net magnetic field created at point M by both wires.

Hint I.1 How to approach the problem

Hint not displayed

Hint I.2 Find the direction of the magnetic field due to wire 1

Hint not displayed

Hint I.3 Find the direction of the net magnetic field

Hint not displayed

Hint I.4 Angle between magnetic field due to wire 1 and the x axis

Hint not displayed

Hint I.5 Find the angle between magnetic field due to wire 1 and the x axis

Hint not displayed

Hint I.6 Net magnetic field

Hint not displayed

Express your answer in terms of , , and appropriate constants.

ANSWER: =

Correct

Part J

Finally, consider point X (not shown in the diagram) located on the x axis very far away in the positive x direction. Which of the vectors best represents the direction of the magnetic field created at point X by wire 1 alone?

Enter the number of the vector with the appropriate direction.

ANSWER: Answer not displayed

Part K

Which of the vectors best represents the direction of the magnetic field created at point X by wire 2 alone?

Enter the number of the vector with the appropriate direction.

ANSWER: Answer not displayed

Problem 33.8

Part A

What current is needed to generate the magnetic field strength of at a point 2.3 from a long, straight wire?

Express your answer using two significant figures.

ANSWER: = 5.8

Correct

Part B

What current is needed to generate the magnetic field strength of at a point 2.3 from a long, straight wire?

Express your answer using two significant figures.

ANSWER: = 580

Correct

Part C

What current is needed to generate the magnetic field strength of at a point 2.3 from a long, straight wire?

Express your answer using two significant figures.

ANSWER: = Answer not displayed

Part D

What current is needed to generate the magnetic field strength of at a point 2.3 from a long, straight wire?

Express your answer using two significant figures.

ANSWER: = Answer not displayed

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#### Solution Preview

Magnetic Field from Two Wires

Learning Goal: To understand how to use the principle of superposition in conjunction with the Biot-Savart (or Ampere's) law.

From the Biot-Savart law, it can be calculated that the magnitude of the magnetic field due to a long straight wire is given by

,

where ( ) is the permeability constant, is the current in the wire, and is the distance from the wire to the location at which the magnitude of the magnetic field is being calculated.

The same result can be obtained from Ampere's law as well.

The direction of vector can be found using the right-hand rule. (Take care in applying the right-hand rule. Many students mistakenly use their left hand while applying the right-hand rule since those who use their right hand for writing sometimes automatically use their "pencil-free hand" to determine the direction of .)

In this problem, you will be asked to calculate the magnetic field due to a set of two wires with antiparallel currents as shown in the diagram . Each of the wires carries a current of magnitude . The current in wire 1 is directed out of the page and that in wire 2 is directed into the page. The distance between the wires is . The x axis is perpendicular to the line connecting the wires and is equidistant from the wires.

As you answer the questions posed here, try to look for a pattern in your answers.

Part A

Which of the vectors best represents the direction of the magnetic field created at point K (see the diagram in the problem introduction) ...

#### Solution Summary

The expert examines current, magnetic fields, vector and biot-savart law in physics.