Magnetic Field and vectors from Two Wires

In summary, the problem involves calculating the magnetic field at point K due to two wires with antiparallel currents. Using the right hand rule, the direction of the magnetic field is determined to be counter-clockwise. The correct vector representation for the magnetic field is vector #3. To find the magnitude of the magnetic field at point L due to wire 1, the Biot-Savart Law is used with the distance between the wires being \sqrt{3}d. To find the magnitude of the net magnetic field at point L due to both wires, the x-components of the magnetic fields from each wire are added together. However, there may be a math error in the calculation.
  • #1
cse63146
452
0

Homework Statement


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 2d. 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.



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.

189576A.jpg
189576B.jpg


Homework Equations



Right Hand Rule for a Straight Wire

The Attempt at a Solution



Using the right hand rule for a straight wire, I found out that the direction of the magnetic field is counter - clockwise. But I'm not sure which vector represents that.

Any suggestions?
 
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  • #2
cse63146 said:

The Attempt at a Solution



Using the right hand rule for a straight wire, I found out that the direction of the magnetic field is counter - clockwise. But I'm not sure which vector represents that.

Any suggestions?

The magnetic field is a vector quantity and has a single direction at a given point. If you draw a magnetic line of force through K, due to the field of wire 1 alone, in which direction does the tangent to the line of force at K point?
 
  • #3
The magnetic field surrounding a current-carrying wire is tangent to a circle centered on that wire. Use the right-hand rule to find which way it points. For the current coming out of the page, point your thumb in the direction of current (out) and your fingers curl in the direction of the field (counter clockwise).
 
  • #4
Vector #8 best describes the direction of the magnetic field.

There's another question that asks: Which of these vectors best represents the direction of the net magnetic field created at point K by both wires?

Since [tex]I_2 = I_1[/tex], the magnetic field due to wire #2 be clock wise and the current due to wire #1 be counter - clockwise, would the vector be #1?
 
  • #5
cse63146 said:
Vector #8 best describes the direction of the magnetic field.

Let's settle this one first.

Draw a circle with the centre at wire 1 and passing through K. Now draw the tangent to the circle at K. Do you still think it's vector #8?
 
  • #6
http://img267.imageshack.us/img267/7536/jhjkkb0.jpg

If I drew that diagram correctly, the answer would be vector #7.
 
Last edited by a moderator:
  • #7
cse63146 said:
If I drew that diagram correctly, the answer would be vector #7.

Think about the right hand rule. The current is coming toward you. It should be #3.

Try the other questions now.
 
  • #8
Thanks, got the other few questions, but I'm having trouble with this one: Point L is located a distance d[tex]\sqrt{2}[/tex] from the midpoint between the two wires. Find the magnitude of the magnetic field created at point L by wire 1.

So I need to use the Biot - Savart Law:

[tex]\frac{\mu_0 I}{2 \pi d}[/tex]

to find the distance, I need to use the pythogorean thereom and I get distance to be [tex]\sqrt{3 d^2} = \sqrt{3} d[/tex] and I would just plug that it for the d in the Biot Savart Law to obtain the equation for the magnetic field of point L by wire 1?
 
  • #9
cse63146 said:
to find the distance, I need to use the pythogorean thereom and I get distance to be [tex]\sqrt{3 d^2} = \sqrt{3} d[/tex] and I would just plug that it for the d in the Biot Savart Law to obtain the equation for the magnetic field of point L by wire 1?

That's it.
 
  • #10
I need to find the magnitude of the net magnetic field at point L in the figure due to both wires and I am having some trouble. I understand that the y components of the magnetic fields from the wires will cancel and just the x components will be left. Therefore, I found the magnitudes of the B_1 field and the B_2 field (magnetic fields due to wires 1 and 2) and used trig to find only the x-components and added these. However, my answer is off by a some factor and I cannot figure out why.

Using t as the angle K-1-L and K-2-L, I got:
B_1x = B_1(sin(t)) = (([tex]\mu[/tex] * I)/(2 [tex]\pi[/tex] d [tex]\sqrt{}3[/tex]) *([tex]\sqrt{}2[/tex] d)/[tex]\sqrt{}3[/tex]d)
B_2x = B_1x

I multiplied B_1x by 2 to get my final answer of:
([tex]\sqrt{}2[/tex][tex]\mu[/tex]I)/(3[tex]\pi[/tex]d)

* note: mu in equations is supposed to be mu sub not and it strangely appears as if 2 and 3 are raised to the pi, they are multiplied

I believe I must have simply made a math error. Any insights would be greatly appreciated! Thank You!
 

Related to Magnetic Field and vectors from Two Wires

1. What is a magnetic field?

A magnetic field is a region in space where a magnetic force can be detected. This force is created by magnetic objects, such as magnets or electric currents.

2. How are magnetic fields created by two wires?

When current flows through a wire, it creates a circular magnetic field around the wire. When two wires are placed parallel to each other and current flows in opposite directions, the magnetic fields of the two wires interact to create a combined magnetic field.

3. What is the direction of the magnetic field created by two wires?

The direction of the magnetic field is determined by the right-hand rule. If you point the thumb of your right hand in the direction of the current in one wire and wrap your fingers around the wire, your fingers will point in the direction of the magnetic field. The same rule applies for the other wire, and the combined magnetic field will be perpendicular to both wires.

4. How does the distance between the two wires affect the magnetic field?

The strength of the magnetic field decreases as the distance between the two wires increases. This is because the force between the two wires becomes weaker as they are further apart.

5. Can the magnetic field from two wires cancel each other out?

Yes, it is possible for the magnetic fields from two wires to cancel each other out if the wires are placed in a specific orientation. This is known as a null point, where the magnetic field is zero.

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