# How Does Earth's Magnetic Field Combine with a Nearby Current-Carrying Wire?

• veroniknstudying
In summary: Now your angle of the Earth field is from horizontal rather than vertical. Don't worry about the wire yet. That angle is 40°. Now, draw the wire in the same profile style. Where does the wire cross the Earth field? Is the wire field pointing up or down at those points?What should happen is that you have a horizontal wire with a field going down from it and a parallel field going up from the other side of the wire. The vector sum of those two fields is vertical. That vertical field is what you need to add to the Earth field to find the total field at the cross point.
veroniknstudying
A long horizontal wire carries 22.0A of current due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth's field there points downward, 40 degrees below the horizontal, and has magnitude 5.0 E-5 T?

My approach:
1. Drew north to the right and the wire lying flat, with current pointing toward right.
2. Used thumb rule to determine that the B field in the front of the wire goes down and the portion behind the wire goes up.
3. Made west above the wire and drew the B field at this point to be pointing directly toward me.
4. <Bk, Bj> where Bk equals ((μI/2pid)+5.0E-5cos(40)) and Bj equals -5.0E-5sin(40).
5. Used pythagorean theorem to find the magnitude of the B field and arctan to find the angle.

I saw other problems online for this, and it seems like my sin and cos may be reversed, but I don't understand why it would be the other way around. If someone can explain that to me, that would be great. The solution is 4.0 E-5 T, 15 degrees below horizontal. This isn't for homework answers. I'm studying for a test, so please feel free to go in depth with explanations and links. Thank you!

Mentor's note: moved form a technical forum.

Hi veroniknstudying,

Welcome to Physics Forums.

Sometimes it can help to try different perspectives for your drawing to make sure that you're using the right angle and trig function. Concentrate on the Earth field alone and draw it in profile. That is, let left to right be S to N as before, but let bottom to top be upwards ##\hat{k}## direction.

## What is net magnetic field?

Net magnetic field is the total magnetic field at a specific point, taking into account the contributions from all nearby sources of magnetic fields.

## How is net magnetic field calculated?

Net magnetic field is calculated by vector addition of the individual magnetic fields at a given point. This involves taking into account the direction and strength of each magnetic field.

## What factors affect the net magnetic field?

The net magnetic field is affected by the strength and direction of the individual magnetic fields, as well as the distance between the magnetic sources and the point of measurement.

## Why is it important to find the net magnetic field?

Finding the net magnetic field is important in understanding the overall magnetic environment of a particular point. This information is crucial in various applications such as navigation, electronics, and medical imaging.

## What are some techniques for finding net magnetic field?

Some techniques for finding net magnetic field include using a magnetic compass, measuring the magnetic field with a magnetometer, or using mathematical equations to calculate the net magnetic field based on the individual magnetic fields.

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