Mark Riley 3107631608 Physics, Nev Clatworthy 1

Magnetic field produced by a current passing

through a conductor

Mark Riley

Task- Practical Report

Aim- I) To investigate the dependence of the magnetic field strength

BI on the current that produces it

II) To investigate the dependence of the magnetic field

strength BI on the distance d from the conductor.

Equipment- Ruler, Protractor, 12 volt battery, wire, Rheostat, magnetic

compass, Ammeter, wooden retort stand, tape

Procedure- See page 4 of the task sheet

Mark Riley 3107631608 Physics, Nev Clatworthy 2

RESULTS

Electric current I = 10.0A

Table 1A

d (cm) θ (0°)

2 75

4 60

6 52

8 42

10 35

12 33

14 26

16 25

18 21

20 20

Graph 1B

𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑤𝑎𝑠 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑖𝑛 𝑐𝑚 ∴ 𝑚𝑒𝑡𝑟𝑒𝑠 = 2 × 10−2

y = 7.3583x - 0.0136R² = 0.997

0

0.5

1

1.5

2

2.5

3

3.5

4

0 1/10 1/5 3/10 2/5 1/2 3/5

tan

θ

1/d

1/d vs tanθ

Mark Riley 3107631608 Physics, Nev Clatworthy 3

QUESTIONS

Q1. Which quantity in this table of results is the dependant quantity?

The angle is the dependant quantity

Q2. Why was the current in each measurement reversed to get the opposite angle

of deflection 𝛉𝟏?

Taking multiple measurements will always produce a more reliable result because an average

can be found and well defined outliers can eliminated. In this experiment two measurements

were made specifically to overcome possible inaccurate readings given by the compass which

would most likely be caused by magnetic fields being present that would interfere with the

magnetic field produced by the current in the wire and or the possibility that the compass was

faulty. The reason as to why the two measurements were taken with the current flowing in

opposite directions which in turn changed the direction of the magnetic field was to eliminate

the great affect that these possible variables may have on the results and can best be explained

with the following example where such variables cause the compass to give a reading 7° out-

Current induces magnetic field and compass reads

25° + 7° = 32°

Current is then made to go in the opposite direction which in turn causes the magnetic field to

be in the opposite direction and the compass reads

-25° + 7° = -18°

An average of the two results is found

32° + 18°

2= 25°

Mark Riley 3107631608 Physics, Nev Clatworthy 4

The error caused by the inaccurate reading given by the compass has been eliminated.

QUESTIONS

Q3a. Plot the appropriate graph of the results that will verify the expected relationship

between 𝐁𝐈 𝐚𝐧𝐝 𝐝.

See Graph 1B

Q3b. Does your graph agree with the theoretical relationship between 𝐁𝐈 𝐚𝐧𝐝 𝐝?

Theoretical relationship is BI =KI

d or BI = KI ×

1

d

For this experiment KI is constant, therefore the theoretical relationship states that 𝐁𝐈 ∝𝟏

𝐝

The trend line from 𝐆𝐫𝐚𝐩𝐡 𝟏𝐁 shows a very close R2 = 0.997 linear relationship

between tanθ and1

d and the value for the y intercept is negligable.

BI = BE tan θ

From the graph tan θ =Gradient

d

∴ BI =BE × Gradient

d or BI = BE × Gradient ×

1

d

Because BE and the gradient are constant, our graph also agrees with the theoretical relationship

−that is that BI is inversely proportional to distance 𝐁𝐈 ∝𝟏

𝐝

Q4. From your graph determine the equation of tanθ in terms of d.

Mark Riley 3107631608 Physics, Nev Clatworthy 5

Using the equation to the trend line in 𝐆𝐫𝐚𝐩𝐡 𝟏𝐁 the equation of tanθ in terms of d is −

tanθ =7.36 × 10−2

d(metres)

QUESTIONS

Q5. ANSWERED IN Q2

Q6. By examining the apparatus and how the measurements were made,

explain why there should be uncertainties in the measure of:

Distance-

Even though much care was taken unavoidable parallax errors would have been present with all

measurements. Limitations of the ruler would also cause uncertainties ±0.5mm

Angle-

Again, although much care was taken, unavoidable parallax errors would have been present

with all measurements of angles. Limitations of the ruler would also cause uncertainties ±0.5°

Adjustments were made to the rheostat to compenstate changes in current that were a result

of the resistance of the wire changing as it heats up. Therefore this was not a factor.

Q7. By comparing the experimentally determined equation in Question 4

relating to tanθ and d to the theoretically determined one using the

equations in the Introduction, calculate the most reliable value for the

Earth’s magnetic field strength 𝐁𝐄

Mark Riley 3107631608 Physics, Nev Clatworthy 6

BI = BEtanθ BI =KI

d ∴ BE tanθ =

KI

d

tanθ =KI

BEd 𝑜𝑟 tanθ =

KI

BE×

1

d 𝑤ℎ𝑒𝑟𝑒

KI

BE= the gradient

∴ 7.36 × 10−2 =KI

BE and BE =

2 × 10−7 × 10

7.36 × 10−2= 𝟐.𝟕 × 𝟏𝟎−𝟓𝑻

QUESTIONS

Q8a. Using the maps attached:

I) What is the magnetic field strength (in Teslas) in Brisbane? 5.5 × 10−5𝑇

II) What is the angle of inclination at Brisbane? 60° South

Q8b. Provide a simple explanation why your experimentally determined

value for 𝐁𝐄 is different to the known value. Show with the appropriate

calculations that you can determine the ‘real’ value for 𝐁𝐄 from the

experimentally determined one.

The compass used in this experiment is constrained to rotate in a horizontal plane only. The

Earths magnetic field has a 60° inclination at Brisbane. Therefore the actual value of the Earths

magnetic field strength would involve the vector addition of more than just the BE from

question 7 which will become BEH in the following diagram.

𝐵𝐸𝑉

𝐵𝐸

Mark Riley 3107631608 Physics, Nev Clatworthy 7

2.7 × 10−5

cos60= 5.4 × 10−5 𝑇𝑒𝑠𝑙𝑎𝑠 60°𝑆𝑜𝑢𝑡ℎ

QUESTIONS

The difference between the Earths field strength found through this experiment compared to

the known value.

5.5 × 10−5 − 5.4 × 10−5 = 0.000001

0.000001

5.5 × 10−5 × 100 = 𝟏.𝟖%

This very small percentage difference along with the close correlation found when plotting the

results Graph 1B shows the very high level of accuracy done in this experiment and uncertainties

of measurements can alone account for this small difference in results.