# Net magnetic field caused by current from two wires

• mm2424
In summary: That's why the angle at P is what you calculated. Now think about the magnetic field at P2, which is very far away. The angle at P2 that the field line makes with the red line is very small. We can use similar triangles to find that angle, which is angle B.
mm2424

## Homework Statement

The attached figure shows, in cross section, two long parallel wires that are separated by distance d = 18.6 cm. Each carries 4.34 A, out of the page in wire 1 and into the page in wire 2. In unit-vector notation, what is the net magnetic field at point P at distance R = 34.2 cm, due to the two currents?

B = iμo/2∏R

## The Attempt at a Solution

(1) The magnetic field lines around wire have a counterclockwise direction. The magnetic field lines around wire 2 have a clockwise direction. When the field lines hit point P, those from wire 1 point to the top right while those from wire 2 point to the bottom right.

(2) Angle a in the diagram is equal to the tan^-1 of 9.3/34.2. Therefore, it = 15.21. This is also the measure of the angle (measured from the x axis) of the tangent of the magnetic field lines at P from both wire 1 and wire 2.

(3) Bnet = 2[iμo/2∏R] = 4.79 x 10^-6 T.

(4) However, only the x components of the magnetic fields survive and add. The y components cancel. Therefore, we must multiply the Bnet by cos(15.21), which yields 4.62 x 10^-6 T.

(5) Because the total net field points to the right, the answer is (4.62 x 10^-6 T)(i hat)

Is this right? I can't find the answer to this question anywhere. Thanks!

#### Attachments

• Chapter29 problem.jpg
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You mostly have the right idea, but I found two problems.
mm2424 said:
(2) Angle a in the diagram is equal to the tan^-1 of 9.3/34.2. Therefore, it = 15.21. This is also the measure of the angle (measured from the x axis) of the tangent of the magnetic field lines at P from both wire 1 and wire 2.
You're correct about angle a, but think more carefully about what angle B makes. It might help to think about a point P2 that is much farther away, where the angle a2 would be very small.

(3) Bnet = 2[iμo/2∏R] = 4.79 x 10^-6 T.
I get something different, but not far off from what you get for Bnet. What are you using for R? You should include a calculation of R in your work.

Also it's really not proper to call this Bnet, which would include the cos(15.21) factor you do later on. I recommend not including the factor of 2, and call this a calculation of B due to one wire.

(4) However, only the x components of the magnetic fields survive and add. The y components cancel. Therefore, we must multiply the Bnet by cos(15.21), which yields 4.62 x 10^-6 T.

(5) Because the total net field points to the right, the answer is (4.62 x 10^-6 T)(i hat)

Is this right? I can't find the answer to this question anywhere. Thanks!
Mostly right, just rethink about the angle for B, and show your calculation of R.

Thanks! Is there a method for figuring out the angle B makes? I was fine when it came to finding the correct angles in kinematics, but I consistently choose the wrong angle in magnetism questions. There might be some geometry rule I've forgotten or something.

The method at play is the basic geometry rules concerning angle measures. Also, realizing that a magnetic field line forms a circle with the wire at the center. That means B (due to wire 1) at point P is at a right angle to the red line in your figure.

Your solution looks correct. The net magnetic field at point P due to the two currents is indeed (4.62 x 10^-6 T)(i hat). Good job using the right-hand rule to determine the direction of the magnetic field lines and considering the x and y components separately. Keep up the good work!

## What is the definition of net magnetic field?

Net magnetic field, also known as resultant magnetic field, refers to the total magnetic field at a specific point in space, which is the sum of all individual magnetic fields that exist at that point.

## How is net magnetic field caused by current from two wires calculated?

The net magnetic field caused by current from two wires is calculated using the right-hand rule, where the direction of the magnetic field is determined by the direction of the current in the wire and the direction of the curl of fingers on the right hand.

## What is the relationship between the distance between two wires and the net magnetic field?

The net magnetic field is inversely proportional to the distance between two wires. This means that as the distance between the wires increases, the net magnetic field decreases, and vice versa.

## How does the direction of current affect the net magnetic field?

The direction of current in the wires affects the direction of the net magnetic field. If the currents in the wires are in the same direction, the net magnetic field will be stronger. If the currents are in opposite directions, the net magnetic field will be cancelled out and there will be no net magnetic field.

## What are some real-life applications of net magnetic field caused by current from two wires?

Net magnetic fields caused by current from two wires have various applications, including electric motors, speakers, and MRI machines. These devices utilize the magnetic fields to produce motion, sound, and medical images, respectively.

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