How Do Magnetic Field Vectors from Parallel Wires Combine?

[dsandhu]

I have racked my brain for the past two hours and I can't figure this out. If anyone can help me with, please do.

Two long parallel wires 6.00 cm apart carry 19.5 A currents in the same direction. Determine the magnetic field strength at a point 12.0 cm from one wire and 13.4 cm from the other. (Hint: Make a drawing in a plane containing the field lines, and recall the rules for vector addition.)

I found the magnetic field for each of the wires separately using B = Mo(I)/ r

but I cannot understand what the "vectors" have to do with the problem.

 

[Doc Al]

I found the magnetic field for each of the wires separately using B = Mo(I)/ r

The magnetic field is a vector: direction matters! The magnitude of the magnetic field surrounding a long, current-carrying wire is $$B = \frac{\mu_0 I}{2 \pi r}$$; the direction is given by the right-hand rule.

The first thing to do is draw a careful diagram so you can figure out the directions of each contribution to the magnetic field. Add them (as vectors, of course) to get the total field at that point.

 

[thepatientmental]

Vectors are used to represent physical quantities that have both magnitude and direction. In this case, the magnetic field strength is a vector quantity, meaning it has both magnitude and direction. In order to accurately determine the magnetic field strength at a point, we need to consider the direction of the field lines from both wires and add them together using vector addition.

In your problem, the two wires are carrying currents in the same direction, which means the magnetic field lines will be parallel and in the same direction. This is important to note because when adding vectors, the direction matters. If the currents were in opposite directions, the magnetic fields would cancel each other out at certain points.

To solve this problem, you need to draw a diagram showing the two wires and the magnetic field lines around them. Then, using the rule for vector addition, you can add the two magnetic field vectors at the point of interest (12.0 cm from one wire and 13.4 cm from the other) to find the total magnetic field strength at that point.

It may also be helpful to use the right-hand rule to determine the direction of the magnetic field around each wire. This will help you accurately add the vectors together.

I hope this explanation helps you understand how vectors are involved in this problem and how to use them to solve it. Good luck!