# Magnetic Field of a Straight Current-Carrying Wire

## Homework Statement

The compass settles at 45 degrees to the NS direction of the earth's field and to the wire it is next to(picture a compass next to a straight upwards wire with a current reduced until the compass points 45 degrees from the current perpendicular to earth's mag field at either north or south). The current measured is 0.731A, and the volts put through it is 2.5V.
Calculate the magnitude and direction of the magnetic field from the current at the compass position (45 degrees). There are five loops of wire.

Also, show the vector diagram of the two magnetic fields and the resultant field (you know the size and direction of the field from the wires, and the angles of the earth's field and the resultant field.) What is the earth's field form your measurements?

## Homework Equations

B=u0I/[2(pi)r]
maybe F=qvBsin(theta)?

## The Attempt at a Solution

I used the B=u0I without the 2(pi)r because no measurements of the wires nor area were given. Using B=uI x 5, I got the answer 4.59 x 10-6T going clockwise.

The vector diagram would show the wire's field going east while the earth's field is going south. I'm completely clueless on the earth's field measurements.

No one can help me?

berkeman
Mentor

## Homework Statement

The compass settles at 45 degrees to the NS direction of the earth's field and to the wire it is next to(picture a compass next to a straight upwards wire with a current reduced until the compass points 45 degrees from the current perpendicular to earth's mag field at either north or south). The current measured is 0.731A, and the volts put through it is 2.5V.
Calculate the magnitude and direction of the magnetic field from the current at the compass position (45 degrees). There are five loops of wire.

Also, show the vector diagram of the two magnetic fields and the resultant field (you know the size and direction of the field from the wires, and the angles of the earth's field and the resultant field.) What is the earth's field form your measurements?

## Homework Equations

B=u0I/[2(pi)r]
maybe F=qvBsin(theta)?

## The Attempt at a Solution

I used the B=u0I without the 2(pi)r because no measurements of the wires nor area were given. Using B=uI x 5, I got the answer 4.59 x 10-6T going clockwise.

The vector diagram would show the wire's field going east while the earth's field is going south. I'm completely clueless on the earth's field measurements.

It's hard to picture the arrangement. You mention a straight wire, but then some number of loops?

Could you maybe scan the problem's diagram and post it? Or post a sketch?

there are no loops, just 5 wires running straight down. i figured that my TA just didn't give me the radius of the wires. This was necessary to calculate the B.

But how do you calculate the earth's mag field? thanks

berkeman
Mentor
there are no loops, just 5 wires running straight down. i figured that my TA just didn't give me the radius of the wires. This was necessary to calculate the B.

But how do you calculate the earth's mag field? thanks

You would just look up the Earth's magnetic field. I think it's somewhere near a Gauss, but it's been a long time since I used that number. Try wikipedia.org, or just a general Google search...

No offense, but if I knew how to post here, I'm pretty sure I knew how to use google.

The earth's magnetic field is somewhere around 5.0x 10^-5 tesla, but if you took your time to read my question, that was not what I was asking for.

Using my derived B and the effect at 45 degrees, find the earth's field. It affects the compass and creates a 45 degree angle at .741 A. Using this information (and lets just say B is 4.87 x 10^-5 as I estimated the radius to be 1.5cm), calculate the earth's field. [A little bit redundant but still readable.]

thanks

berkeman
Mentor
No offense, but if I knew how to post here, I'm pretty sure I knew how to use google.

The earth's magnetic field is somewhere around 5.0x 10^-5 tesla, but if you took your time to read my question, that was not what I was asking for.

Using my derived B and the effect at 45 degrees, find the earth's field. It affects the compass and creates a 45 degree angle at .741 A. Using this information (and lets just say B is 4.87 x 10^-5 as I estimated the radius to be 1.5cm), calculate the earth's field. [A little bit redundant but still readable.]

thanks

I'm still pretty lost without a diagram, but okay. (BTW, your original post said 0.731A, but you have 0.741A in the post above this one.)

Anyway, you know the equation to calculate the B field some radius away from a long wire, and it from the geometry you can show a vector sum of the two B-fields. What is the part that you are having trouble with? (Sorry if I'm not catching on very well here)

Sorry it's 0.731A; i typoed. I'm having trouble figuring out the earth's magnetic field from this equation. I don't know how to make an image on here so I'll try to explain it as easily as possible and how it was done in lab.

It's kind of like this configuration http://www.exploratorium.edu/snacks/circles_magnetism_I/index.html" [Broken] except it's not a battery and we could adjust the voltage and current. The rig we used had a box instead of the Tinkertoy set.

Theres a box open ended and a bundle of 5 wires going across the opening from one sides middle to the opposite sides middle. Perpendicular to these wires is a piece of paper in the middle of the box (separating the box into two sections and a hole is poked so the wires can go through it). The purpose of this paper divider is to have a place for the compass to rest. The compass is put next to the wires, and it obviously points perpendicularly to the field when the volts are at 2.5V and current at max, so it points tangent to the wires. The compass was placed at the point where the current is perpendicular to the earth's magnetic field, which is North/South (as opposed to East/West). The current was then reduced until the angle of the compass (which was perpendicular at max current 1.967A) became 45 degrees to that relative position. The current recorded was 0.731A. Since at 0 Current, the red side of the compass would point North, it is logical that the combined magnetic fields of the earth and the current in the 5 wires made it 45 degrees. I want to know how to calculate the earth's magnetic field with this information.

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with this new information is there anyone who would like to take a stab at solving the earth's field with my measurements?