At the dot above Wire 1, the net magnetic field is zero due to the cancellation of opposite directions. At the dot below Wire 2, the net magnetic field is counterclockwise and twice as long as B₂, reflecting vector addition.
Formula for Magnetic Field (B):
Recall the formula for the magnetic field (B) around a long straight wire carrying a current (I):
B = μ₀I / (2πr)
where μ₀ is the permeability of free space, and r is the distance from the wire.
Right-Hand Rule:
Use the right-hand rule to determine the direction of the magnetic field at each dot. Point your thumb in the direction of the current, and curl your fingers around the wire. The direction of your fingers is the direction of the magnetic field.
Draw Magnetic Field Vectors:
Draw magnetic field vectors at each dot using a black pen. Label them as B₁ and B₂ for each wire. The length of the vector should be proportional to the magnitude of the magnetic field, which depends on the distance from the wire.
Vector Addition:
Use vector addition to find the net magnetic field at each dot using a red pen. Draw the resultant vector from the tail of the first vector to the head of the second vector. Label it as B_net. The direction and magnitude of the net magnetic field depend on the relative orientation and strength of the individual magnetic fields.
Example Diagram:
Visualize the magnetic fields for each wire and the net magnetic field at specific points. Use symbols (e.g., 'x' for current into the page and 'o' for current out of the page) to represent the direction of the current.
Dot above Wire 1:
B_net = 0 (cancellation of opposite directions)
Dot below Wire 2:
B_net = Counterclockwise and twice as long as B₂