Joining two wires, magnetic fields and a little algebra

In summary, when two wires are joined together, the strength of the magnetic field can increase. The direction of the current flowing through the wires determines the direction of the magnetic field. There is a specific formula, B = μ0 * I / (2π * r), that can be used to calculate the strength of the magnetic field when two wires are joined. Algebra can also be used to manipulate this formula to determine optimal distance and current for a desired magnetic field. Additionally, the magnetic field created by joining two wires can be controlled and manipulated by adjusting the current and distance between the wires, making it useful for applications such as electromagnets and electric motors.
  • #1
shyguy79
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Homework Statement


Consider a general point on the line joining the two wires and a distance d
away from the mid-point O. By summing the magnetic field due to currents of magnitude i flowing in both the wires which are non-zero, show that on the line joining the two wires, the magnetic field strength is given by:

B= μ iD / π(D2 −d2)

Homework Equations


(D^2 −d^2) = (D+d)(D-d) ****** a simple trig identity
B= μ i / 2π d

The Attempt at a Solution


I'm kinda stuck - any pointers on where to start?
 
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  • #2
Just bumping it back up - anyone any ideas?
 

1. Can two wires be joined together to create a stronger magnetic field?

Yes, joining two wires can increase the strength of the magnetic field. When two wires are placed parallel to each other and the current flows in the same direction, they will produce a stronger magnetic field compared to a single wire.

2. How does the direction of the current affect the magnetic field when joining two wires?

The direction of the current flowing through the wires determines the direction of the magnetic field. When joining two wires, the current should flow in the same direction to create a stronger magnetic field.

3. Is there a specific formula to calculate the strength of the magnetic field when joining two wires?

Yes, the strength of the magnetic field when two wires are joined can be calculated using the formula B = μ0 * I / (2π * r), where B is the magnetic field strength, μ0 is the permeability of free space, I is the current flowing through the wires, and r is the distance between the two wires.

4. How can algebra be used when joining two wires and examining the magnetic field?

Algebra can be used to manipulate the formula for calculating the magnetic field strength when two wires are joined. This can help determine the optimal distance between the wires and the necessary current to achieve a desired magnetic field strength.

5. Can the magnetic field created by joining two wires be controlled or manipulated?

Yes, the magnetic field can be controlled and manipulated by adjusting the current flowing through the wires and the distance between them. This can be useful in various applications such as electromagnets and electric motors.

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