What is the Magnetic Field at Point P due to Two Parallel Wires?

In summary, the magnetic field at point P due to the current in the lower wire is x= -Bcos 30, y= -Bsin 30, and z= 0.
  • #1
Angie K.
108
1

Homework Statement



HW14_4.jpg


Two long thin parallel wires a distance d = 14.6 cm apart carry 25-A currents (I) in the same direction. The magnetic field is measured at point P, a distance d1 = 12.1 cm from the lower wire and a distance d2 = 5.8 cm from the upper wire.

a. Find the x and y components of the magnetic field at P due to the current in the lower wire only.

b. Find the x and y components of the magnetic field at P due to the current in the upper wire only.

c. Determine the magnitude |B| of the total magnetic field at P.

Homework Equations



B = mu0/2 pi * I/d

The Attempt at a Solution


[/B]
to find B1x :

= -Bcos 30

-mu0/2*pi *25/.121 *sqrt3/2

this isn't the right answer, since the rest of the problems are the same way, I need to make sure I understand what I'm doing wrong before moving on. Someone please help!
 
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  • #2
Did you draw the picture? From the given information there are two points that satisfy the given info.

Suggestion, draw the diagram above with the magnetic field vectors at point p from both wires. The magnitudes of the vectors is easy, and you should know the general directions of both vectors, the rest is trig.?
 
  • #3
Spinnor said:
Did you draw the picture? From the given information there are two points that satisfy the given info.

Suggestion, draw the diagram above with the magnetic field vectors at point p from both wires. The magnitudes of the vectors is easy, and you should know the general directions of both vectors, the rest is trig.?

Wouldn't the field be going the same way from both wires? Then what would the x and y look like if the field is just one on top of the other going the same way?
 
  • #4
The two vectors will be approximately perpendicular at point p, right? Draw the magnetic field lines that go around each wire and also go through point p from each current, they are circles, right?
 
  • #5
Spinnor said:
The two vectors will be approximately perpendicular at point p, right? Draw the magnetic field lines that go around each wire and also go through point p from each current, they are circles, right?

The field lines are going to the left on both wires. so I'm confused what direction they would be at point P
 
  • #6
The magnetic field from the top wire will be pointing roughly in the 1o'clock direction and the field other wire will point in roughly the 10 o'clock direction?
 
  • #7
Angie K. said:

Homework Statement



HW14_4.jpg
Where did you get the 30 degrees? Careful, this is not a right-angled triangle.
Suggestion: determine the three inner angles first.
 
  • #8
concentric1.jpg


Like this but reverse the red arrow.
 

FAQ: What is the Magnetic Field at Point P due to Two Parallel Wires?

1. What is the magnetic field of two parallel wires?

The magnetic field of two parallel wires is dependent on the distance between the wires, the current flowing through each wire, and the direction of the currents. When the currents are flowing in the same direction, the magnetic fields will add and create a stronger field between the wires. When the currents are flowing in opposite directions, the magnetic fields will cancel out, resulting in a weaker field between the wires.

2. How is the direction of the magnetic field determined for two wires?

The direction of the magnetic field for two wires can be determined by using the right-hand rule. Point your right thumb in the direction of the current flow in the first wire, then curl your fingers towards the direction of the current flow in the second wire. The direction your fingers point in is the direction of the magnetic field between the wires.

3. What is the mathematical equation for calculating the magnetic field between two wires?

The mathematical equation for calculating the magnetic field between two wires is B = (μ0 * I1 * I2) / (2 * π * d), where B is the magnetic field, μ0 is the permeability constant, I1 and I2 are the currents in each wire, and d is the distance between the wires.

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

The distance between two wires has an inverse relationship with the magnetic field. As the distance between the wires increases, the magnetic field decreases. This is because the magnetic field follows an inverse square law, meaning it decreases by the square of the distance.

5. Can the magnetic field of two wires be manipulated?

Yes, the magnetic field of two wires can be manipulated by changing the distance between the wires or by changing the direction or magnitude of the currents flowing through the wires. Additionally, using a third wire with a current flowing in a specific direction can also alter the magnetic field between the two wires.

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