# How to find the magnetic force on a current-carrying tube in a neon sign?

• SHOORY
In summary: If you crawl along the tube, then doesn't each tiny step take you in the direction of the tube and never perpendicular to the tube? Yes.
SHOORY
1. The problem statement, all variables, and given/known data
Assume the Earth’s magnetic field is 52.0 mT northward at 60.08 below the horizontal in Atlanta, Georgia. A tube in a neon sign stretches between two diagonally opposite corners of a shop window—which lies in a north-south vertical plane—and carries current 35.0 mA. The current enters the tube at the bottom south corner of the shop’s window. It exits at the opposite corner, which is 1.40 m farther north and 0.850 m higher up. Between these two points, the glowing tube spells out DONUTS. Determine the total vector magnetic force on the tube
How to solve this equation I just don't know
how to do S letter in DONUTS
how to integrate to find its length

SHOORY said:

## Homework Equations

This is a good place to start. What vector equations have you been taught relating magnetic field, current and force?

haruspex said:
This is a good place to start. What vector equations have you been taught relating magnetic field, current and force?
F=integration of I B sin theta ds

f
haruspex said:
This is a good place to start. What vector equations have you been taught relating magnetic field, current and force?
for D O the total force is zero because it is closed

haruspex said:
This is a good place to start. What vector equations have you been taught relating magnetic field, current and force?
so now we have to find the force on N U T S
I think for N and T it is easy but U S needs theta and I have a problem thinking of the limits of the theta in the integration

SHOORY said:
F=integration of I B sin theta ds
For the vector force, you would have ##\vec F = \int \left( I \vec {dL} \times \vec B \right)##
Try to show that the integral gives the same result no matter what word is spelled-out by the tube in the neon sign.

SHOORY
TSny said:
For the vector force, you would have ##\vec F = \int \left( I \vec {dL} \times \vec B \right)##
Try to show that the integral gives the same result no matter what word is spelled-out by the tube in the neon sign.
how is that? I mean isn't that... I don't know
so you mean that we ignore the letters and treat it as a rectangle or something

SHOORY said:
how is that? I mean isn't that... I don't know
so you mean that we ignore the letters and treat it as a rectangle or something
Well, you need to show that you can ignore the particular shapes of the letters.

The idea is to simplify the integral ##\vec F = \int \left( I \vec {dL} \times \vec B \right)## by factoring out any constant factors.

Last edited:
To help you a bit with what post 8 suggests, pretend you're a bug crawling along the tube from one end to the other. You can take any path you like, but you're a smart bug so for each tiny step you take you keep track of the distance traveled in the direction of the tube and the distance traveled perpendicular to the tube. You do that algebraically, resolving each tiny move you make into components parallel and perpendicular to the tube. You can travel any way whatsoever but you must end up at the other corner of the window.

When you separately add up all the + and - parallel and perpendicular steps, what do you get for total net travel alongside & perpendicular to the tube?

rude man said:
To help you a bit with what post 8 suggests, pretend you're a bug crawling along the tube from one end to the other. You can take any path you like, but you're a smart bug so for each tiny step you take you keep track of the distance traveled in the direction of the tube and the distance traveled perpendicular to the tube.

rm, If you crawl along the tube, then doesn't each tiny step take you in the direction of the tube and never perpendicular to the tube?
Did you mean parallel or perpendicular to the diagonal of the window?

TSny said:
Did you mean parallel or perpendicular to the diagonal of the window?
Yes.
You can go forwards and backwards, left and right, along the diagonal, all you want, long as you wind up in the other corner. Of course, your net travel has to be forwards in order for you to get from one diagonal corner to the other. Sorry I wasn't too clear on that.

## 1. What is magnetic force?

Magnetic force is a type of non-contact force that acts between two or more magnets, or between a magnet and a magnetic material. It is responsible for the attraction or repulsion of objects due to their magnetic properties.

## 2. How is magnetic force related to electric current?

Magnetic force and electric current are closely related. Whenever there is an electric current flowing through a wire, a magnetic field is created around the wire. This magnetic field can then interact with other magnetic fields to produce a force.

## 3. What factors affect the strength of a magnetic field?

The strength of a magnetic field is affected by the distance from the source of the field, the size and strength of the magnets or magnetic materials involved, and the alignment of the magnetic fields.

## 4. How is the direction of magnetic force determined?

The direction of magnetic force is determined by the relative orientation of the magnetic fields of the objects involved. Like poles (north to north or south to south) repel each other, while opposite poles (north to south) attract each other.

## 5. What are some real-life applications of magnetic force and field?

Magnetic force and field have many practical applications, including in generators, motors, speakers, and MRI machines. They are also used in magnetic levitation technology and in compasses for navigation.

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