# Investigating the effect of magnetic force on a current carrying wire

1. Dec 27, 2007

### jdiamonddiva

[SOLVED] investigating the effect of magnetic force on a current carrying wire

1. The problem statement, all variables and given/known data
The aim of this experiment is to investigate the magnetic force of a current-carrying wire. In this experiment we will investigate the effect of current and to do this one shall measure the force on a current-carrying wire placed in a uniform magnetic field.

2. Relevant equations

Magnetic field strength is defined as:
‘the force per unit length per unit current on a current-carrying conductor at right angles to the direction of the magnetic field.’
When the charges pass through uniform magnetic field they experience a magnetic force. The total magnetic force on the wire is calculated by
B=F/Il where F = Force in Newtons, B= magnetic field strength measured in Tesla and l = length measured in meters.
The term B is called the magnetic field strength, or the flux density, and is measured in Tesla, T. The magnetic flux density can be thought of as the concentration of field lines. We can increase the force by increasing any of the terms within the equation. If we coil up the wire, we increase its length within the magnetic field
To investigate this further an experiment can be conducted to show the dependence of the force on a current-carrying wire in a magnetic field.

3. The attempt at a solution

Method explained:

- A ‘u’ shaped magnet is formed by placing two Magnadur magnets on a steel yoke with opposite poles facing each other.

- The magnet is then placed on the top-pan balance and the balance is then zeroed. The ‘top pan balance’ is a straightforward way of investigating the factors affecting

- The force on a wire carrying a current in a magnetic field. The ‘wire’ is clamped so that it remains stationary and the balance measures the ‘change in weight’ of the Magnadur magnets placed on its pan.

- A variable current source is connected to the current balance assembly, which has at one end a removable wire loop etched onto a circuit board. This wire loop is then placed into the permanent magnet assembly so the wire loop is perpendicular to the magnetic field but is not touching the magnets.

- When a current flows through the wire loop, a magnetic force is created. Since the wire loop is stationary the magnetic force acts on the permanent magnet assembly causing its weight to either increase or decrease depending on the direction of the current and the orientation of the magnetic field. The change in the balance reading is due to the magnetic force given by the equation that will be expanded upon later.

- The balance reading is then to be recorded at 0.5 intervals of current (this is altered using the variable resistor)
- One gram is equivalent to a weight of 0.0098 N (0.01 N will probably be accurate enough for this experiment).

Control of Variables
In this experiment it is important to keep variables controlled in order to make this a fair test. There are three variables to consider in this experiment and they are as follows:
1. The length of wire may be varied by exchanging one wire loop for another.
2. The current amplitude may be varied by adjusting the output from the power supply. (The direction of the current flow may also be altered.)
3. The strength of the magnetic field may be altered by varying the number of horseshoe magnets in the magnet assembly. (The direction of the magnetic field may also be altered.)
In this current experiment it is the current that is being investigated and therefore that is the independent variable that will allow us to get different balance readings (dependent variable.) It is important to keep therefore, the length of the wire and the strength of the magnetic field constant. To ensure this I have ensured that there are only two magnadur magnets and that the wire is a set length of 1 metre. It is also important for the wire to have a uniform cross-sectional area, as this increases the surface area of the wire and thus means that the accuracy of the answer will change accordingly
Precautions for accuracy
All school experiments and in fact all experiments conducted by people are all vulnerable to human error and this must be accounted for in order to gain as accurate result as is possible.
In this experiment in order to do this the following was done:

- the temperature of the room was kept note of at all times as to any unusual changes that may effect the experiment, this did not prove to be an issue.
- All balance readings were taken into consideration as +/- 0.01g
- Two readings were taken each time and an average conducted for further accuracy
- The power supply was turned off after each reading to ensure that the wire could return to room temperature after having current passed through it to ensure a more accurate reading.
-
Precautions for safety
1. Caution!!! A rheostat has been added into the circuit for safety precautions to ensure the current does not get too hot and thus the rod too hot.
2. The power supply should be set to constant current mode. To do so, turn the DC VOLTAGE ADJUST knob fully clockwise, then adjust the DC CURRENT ADJUST knob to obtain the desired output current.
Range and number of readings.
Using an ammeter of range 0 –5 ampere two readings at each 0.5 interval was taken to give a total of 18 readings.

As with all physics laboratory experiments, one must be careful to use the appropriate units. If all forces (i.e., the magnetic force and weight) are measured in newtons ( ), charges in coulombs ( ), and velocities in meters per second ( ), then as we will see in the explanation the unit of the magnetic field is given as newton per coulomb-meter per second. In SI units this is known as the tesla ( ).

i have done some results but need help with the graph, conclusion and evaluation just need some guidance could i possibly email my investigation to someone and ask for their hlep? thank you

2. Dec 28, 2007

### Kurdt

Staff Emeritus
I would have personally repeated measurements at least three times so one could calculate the error. The graph should be a simple straight line graph. The gradient of which will be the magnetic field times the length of wire in the magnetic field. Your conclusion should state what the experiment has told you about the relationship between current, magnetic field and force referencing your results. The evaluation will be how well you think the experiment was conducted and any improvements you'd make on future experiments.

3. Dec 28, 2007

### jdiamonddiva

Thank Yoo For The Help Thats Great! What Do I Plot On The Axes? X

4. Dec 28, 2007

### Kurdt

Staff Emeritus
The dependent variable is usually the y-axis in this case that will be force I assume. Then the independent variable will be the x-axis, which is current.

5. Dec 28, 2007

### jdiamonddiva

i have a bit of a problem though because to change the balance readings from g into force (N) ive multiplied by 0.01 is this right becuase now i have readings of

8.9 x 10-4

1.62 x 10-3

2.35 x 10-3

2.98 x 10-3

3.92 x 10-3

and im not sure what sort of scale i can plot these on?

4.83 x 10-3

5.52 x 10-3

6.25 x 10-3

6. Dec 28, 2007

### Kurdt

Staff Emeritus
What you'll want is the effective weight. Since weight ($W=mg$) is a force, you will need to multiply by g not 0.01.

7. Dec 28, 2007

### jdiamonddiva

i really dont understand so say the current is 3.0a and the balance reading is 0.483g how would i change the 0.483g into a force??

8. Dec 28, 2007

### Kurdt

Staff Emeritus
First did you weigh the wire without the field?

Secondly one would turn the grams into kilograms (thats probably what you were trying above apologies for not recognising that) and multiply by the acceleration due to gravity to get the weight. Then you'd have to subtract the weight of the wire with no field, to find the force due to the field.

9. Dec 28, 2007

### jdiamonddiva

no because - One gram is equivalent to a weight of 0.0098 N and so i round this to 0.01?

10. Dec 28, 2007

### andrevdh

Correct for calculating the force. Probably best to keep the two significant digits that is multiply the mass reading in grams by 0.0098 to get the force that the magnets experienced, whic is the same as what the wire experienced.

What is worrying me a bit that the balancing circuit of electronic scales uses coils, which could be influenced by your setup.

11. Dec 28, 2007

### Kurdt

Staff Emeritus
OK thats fine. I just didn't realise because there were no units.

Scale for the graph should be fairly simple if you note that 8.9x10-4 = 0.89x10-3. So you can then have a scale from 0 - 7 x10-3.

12. Dec 28, 2007

### jdiamonddiva

thats brilliant thank you also, i noticed when i calculated the magnetic field strength by doing force divided by (current x length) i found the following results:
1.78 x 10-3

1.62 x 10-3

1.57 x 10-3

1.49 x 10-3

1.57 x 10-3

1.61 x 10-3

1.57 x 10-3

1.56 x 10-3

why does the values go down and then up again? x

13. Dec 28, 2007

### Kurdt

Staff Emeritus
There'll be a certain amount of experimental error that will make the value fluctuate slightly.

14. Dec 28, 2007

### andrevdh

There is only a 6 per cent variation in the strength of the magnetic field according to your values. Not really cause for concern.

15. Dec 28, 2007

### jdiamonddiva

so would i say generally that the magnetic force is increasing or decreasing

16. Dec 28, 2007

### andrevdh

What you have calculated is the strength of the magnetic field due to the presense of the magnets on the pan, not the magnetic force. The slight variation in the strength is not significant and are most likely caused by other factors, maybe there were a slight breeze over the pan which influenced the reading (Bernoulli effect), or the scale were moved sligthly during readings causing it to go slightly out of level (or because you leaned on the bench and distorted the surface) .....

17. Dec 28, 2007

### jdiamonddiva

oh i see, now i understand soo the magnetic field strength really had nothing to do with the experiment at all!! ok so to improve my experiment i could

do more readings to improve accuracy
investigate about the coils in the balance
anything else?

18. Dec 28, 2007

### andrevdh

you could change the strength of the magnetic field by changing the amount of magnets.

to investigate the possibility of the setup influencing the reading on the scale you can put the magnets on say a plastic container on the scales. That would position them further away from the electronics in the scale.

taking more readings would decrease the spread in values, that is the spread around the average value should become smaller - the distribution becomes more concentrated around the average value for a particular reading.

19. Dec 28, 2007

### jdiamonddiva

thank you so much for your help you have an absloute life saviour by filling in the gaps that i didnt understand! so here is the final conclusion could you tell me if this is correct and/or i could add anything else....(in the process of writing the evaluation!!)

'from the above tabular column and from my graph we see that the current passed through the wire is directly proportional to the magnetic field when the length of the wire and the temperature of the room and strength of the magnets remain constant because the values of the magnetic force increases as the current increases, and we can see this from the gradient of the graph, therefore my prediction was correct.

It is evident therefore, that there is a clear relationship between current in a wire and magnetic lines of force. If we send current through a wire, we generate magnetic lines of force that rotate around the wire. The more current, the more the lines of force expand out from the wire.

The deflecting force that a magnet exerts on a current-carrying wire is the mechanism behind the operation of most electric motors. Moreover, the reverse effect is also true: if I move a loop of wire across the pole of a magnet, a current will also begin to flow in the wire.

We can also note that The magnitude of magnetic field produced by a straight current-carrying wire at a given point is Directly proportional to the current passing in the wire because the gradient of the graph represents the magetic field strength x length of the wire. However it is noticeable from my results that there are some irregularities as there is slight variation in the strength of the magnetic field however these is not significant and are most likely caused by other factors most possibly due to human error. For example there may have been a slight breeze over the pan which influenced the reading (this is called the Bernoulli effect), or the scale may have been moved slightly during readings causing it to go slightly out of level and fluctuate a little. Overall the readings fluctuate by about 6% so there is nothing that should completely alter the findings of my results but is certainly something to consider should I do the experiment again.'

20. Dec 28, 2007

### andrevdh

you shoould limit your conclusion to only that what you investigated in the experiment. do not include "known" theory that you did not actually verify yourself. also I think one generally state the relationship in the form y is directly proportional to x, in your case the magnetic force (Lorentz force?) that the wire experiences is directly proportional to the curent that flows through it. I think one should not take the idea of "amount of magnetic field lines" too seriously. these lines are abstract lines which helps us to visualize trhe field.

on second thought you could also investigaste the effect of length of the conductor in the field on the force that it experiences by changing the length of the yoke. that is the magnetic field woudl appear only al;ong the length of the yoke (if the lenght of the poles is shorter than the yoke). this is because the magnet magnetizes the whole lenght of the yoke. the regions in the material of the yoke align themselves along its whole length, irrespective of how "long" the actual pole is that magnetizes it. In this case you would keep the current constant and vary the length and again get the force as the dependent variable.