Where to Start Solving Magnetic Field of Two Wires

  • Thread starter cwtliew
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In summary, if a long straight wire carrying current I is placed along the x-axis and another long straight wire carrying current I/2 is placed along the y-axis, the combined magnetic field will be zero at points where the fields due to each wire are equal and in opposite directions. This can be determined by setting the fields from each wire equal at an arbitrary point (x,y) and solving for y in terms of x. The equations used to solve this problem are Ampere's Law and the Biot-Savart Law.
  • #1
cwtliew
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Homework Statement



a long straight wire lying along the x-axis carries current I flowing in the +x direction. A second long straight wire lying along the y-axis carries current I/2 in the +y direction.
where is their combined magnetic field zero?

Homework Equations



Ampere's Law/biot-savart law

The Attempt at a Solution



where do i begin??
pls help.thanks.
 
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  • #2
What is the magnetic field due to a current of wire?

Look at each of the quadrants in the xyplane... examine the direction of fields due to each of the two wires... in which quadrants are they in the same direction? in which quadrants are they in the opposite direction...

now within the quadrants where the fields are in opposite directions... you need the magnitude of the two fields to be equal (so that they cancel each other out)...

take an aribtrary point (x,y)... what is the field at this point due to the first wire... and due to the second wire... set the two fields equal... solve for y in terms of x.
 

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

The formula for calculating the magnetic field of two parallel wires is given by B = μ0I/2πd, where B is the magnetic field, μ0 is the permeability of free space, I is the current in the wires, and d is the distance between the wires.

2. How do I determine the direction of the magnetic field?

The direction of the magnetic field is determined by the right-hand rule. Point your right thumb in the direction of the current in one wire, and your fingers will curl in the direction of the magnetic field.

3. Can the magnetic field of two wires cancel each other out?

Yes, the magnetic field of two wires can cancel each other out if the currents in the wires are flowing in opposite directions. This is known as a zero net magnetic field.

4. What happens to the magnetic field when the distance between the wires is increased?

When the distance between the wires is increased, the magnetic field decreases. This is because the magnetic field is inversely proportional to the distance between the wires.

5. How does the current in the wires affect the strength of the magnetic field?

The strength of the magnetic field is directly proportional to the current in the wires. This means that if the current increases, the magnetic field also increases.

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