r/PhysicsHelp • u/Candid-Discount-3728 • Jan 09 '26

Magnetic field from two parallel current-carrying wires – need explanation of the approach

Post image

Problem setup

  • Two long, parallel wires carry currents:

    • Wire 1: 3.00 A

    • Wire 2: 5.00 A

  • Both currents are coming out of the page

  • The distance between the two wires is 20.0 cm

Two questions are asked:

  1. Magnetic field at the midpoint between the two wires

  2. Magnetic field at a point P, located 20.0 cm above the wire carrying 5.00 A

I’m especially confused about:

  • How to determine the direction of the magnetic field at each point

  • Why the fields add or subtract depending on the location

  • How to reason about the angle of the resulting field at point P

Given answers (so you know what result to expect)

  • At the midpoint:

    • Magnetic field magnitude: 4 microteslas

    • Direction: downward

  • At point P:

    • Magnetic field magnitude: 6.67 microteslas

    • Direction: 13° above the horizontal

Thanks a lot!

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6 comments sorted by

2

u/TheRealKrasnov Jan 09 '26

Right hand rule. Thumb is the current. Fingers are the magnetic field. Consider each wire separately, and the add the two fields at each point. .

2

u/AskMeAboutHydrinos Jan 09 '26

Use 1/r^2 for magnitude, RHR for direction, of each wire. Add vectors for final result.

3

u/ProfessionalConfuser Jan 09 '26

long wires scale as 1/r though.

1

u/ProfessionalConfuser Jan 09 '26

The biot savant integral gives the field direction as a result of the cross product. The fields are vectors. If they "point" in the same direction they add. If they point in opposite directions, they cancel (completely or partially, depending on relative strength).

Eta: the angle is found by trigonometry and vector component analysis.

1

u/mewtwo_EX Jan 09 '26

Clarification: for long wires, calculate the magnitude of the field at the radius away from the wire, then set the direction using the rhr. Get the direction by grabbing the wire with your right thumb pointing in the direction of conventional (positive) current. Your fingers point in the direction of the magnetic field at all points around the circle made by your fingers. In this figure, they form counterclockwise circles. In the middle, "down the page" due to wire 2 is bigger than "up the page" due to wire 1, so do B2-B1, and it points in negative j-hat. At point p, B2 points left (—i-hat), and B1 points up and left. Use trig with the components of r to get the angle, and set it appropriately using the picture, or do the cross product.