How Do Magnetic Field Vectors from Parallel Wires Combine?

• dsandhu
In summary, the conversation discusses the calculation of the magnetic field strength at a point between two parallel wires carrying currents in the same direction. The hint is to make a drawing and use the right-hand rule for vector addition. The formula for the magnetic field is B = \frac{\mu_0 I}{2 \pi r} and the direction is important. The total field can be calculated by adding the contributions from each wire as vectors.
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 seperately using B = Mo(I)/ r

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

dsandhu said:
I found the magnetic field for each of the wires seperately 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.

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!

1. What is a magnetic field vector?

A magnetic field vector is a physical quantity that describes the direction and strength of a magnetic field at a specific point in space. It is represented by an arrow, with the direction of the arrow indicating the direction of the magnetic field and the length of the arrow representing the strength of the field.

2. How is a magnetic field vector measured?

A magnetic field vector can be measured using a device called a magnetometer, which detects and measures the strength and direction of magnetic fields. It can also be calculated using mathematical equations based on the properties of the source of the magnetic field.

3. What factors can affect the direction and strength of a magnetic field vector?

The direction and strength of a magnetic field vector can be affected by factors such as the distance from the source of the field, the properties of the material the field is passing through, and the presence of other magnetic fields nearby.

4. How are magnetic field vectors used in everyday life?

Magnetic field vectors have many practical applications in everyday life, such as in compasses, electric motors, and generators. They are also used in medical imaging techniques like MRI machines, and in technologies like magnetic levitation trains.

5. Can magnetic field vectors be manipulated?

Yes, magnetic field vectors can be manipulated using various techniques, such as by changing the strength of an electric current flowing through a wire, or by using permanent magnets with specific shapes and orientations. This manipulation is the basis for many technologies that rely on magnetic fields.

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