000 Bfield ENG rev5 20160901 - Yonsei Universityphylab.yonsei.ac.kr/exp_ref/205_Bfield_ENG.pdf ·...

General Physics Lab (International Campus) Department of PHYSICS YONSEI University

Lab Manual

Magnetic FieldsVer.20160901

Lab Office (Int’l Campus)

Room 301, Building 301 (Libertas Hall B), Yonsei University 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA (☏ +82 32 749 3430) / 18

[International Campus Lab]

Magnetic Fields

Determine the strength of the magnetic field in the region of various current-carrying conductors.

1. Magnetic Field of a Moving Charge

A moving charge produces a magnetic field. The magnitude

of the magnetic field of a single point charge moving with a

constant velocity at the point , as shown in Fig. 1, is pro-

portional to | |, 1⁄ , , and sin .

4

| | sin (1)

4 10 N ⋅ s /C 4 10 T ⋅ m/A

Magnetic field is a vector field. We use the symbol for

magnetic field. is perpendicular to the plane of and ,

where represents the position of the field point in relation

to the source point and is the velocity of the charge. The

direction of is determined by the right-hand rule.

We can incorporate both the magnitude and direction of

into a single vector equation using the vector product.

4

(2)

where the unit vector / .

The SI unit of is the tesla (T).

1 T 1 N ⋅ s/C ⋅ m 1N/A ⋅ m 10 gauss

Fig. 1 Magnetic field vectors due to a moving positive point charge . At each point, is perpendicular to the plane of and , and its magnitude is proportional to the sine of the angle between them.

Objective

Theory

----------------------------- Reference --------------------------

Young & Freedman, University Physics (14th ed.), Pearson, 2016

28.1 Magnetic Field of a Moving Charge (p.945~948)

28.2 Magnetic Field of a Current Element (p.948~950)

28.3 Magnetic Field of a Straight Current-Carrying Conductor (p.950~952)

28.5 Magnetic Field of a Circular Current Loop (p.954~957)

28.7 Applications of Ampere’s Law (p.960~963)

-----------------------------------------------------------------------------


Lab Manual




2. Magnetic Field of a Current Element

The total magnetic field caused by several moving charges

is the vector sum of the fields caused by the individual charg-

es. We can use this principle of superposition of magnetic

fields to find the field produced by a current in a conductor.

The volume of a short segment of a current-carrying

conductor is , where is the cross-sectional area of the

conductor, as shown in Fig. 2. If there are moving charged

particles per unit volume, each of charge , the total moving

charge in the segment is

(3)

The moving charges in this segment are equivalent to a

single charge , traveling with a velocity equal to the drift

velocity . From equation (1) the magnitude of the resulting

field at any field point is

4

| | sin4

| | sin (4)

The element | | of equation (4) equals current . So

4

sinor

4

(5)

Equation (5) is called the law of Biot and Savart.

Fig. 2 Magnetic field vectors due to a current element .

3. Magnetic Field

of a Straight Current-Carrying Conductor

Fig. 3 shows a straight current carrying conductor with

length 2 carrying a current . We will find the magnetic field

at a point a distance from the conductor on its perpen-

dicular bisector. Substituting , and

sin sin ⁄ into equation (5) and inte-

grating this yields

4 ⁄ 4

2

√ (6)

When the length 2 of the conductor is very great in com-

parison to its distance from point , we can consider it to

be infinitely long. In the limit ⟶∞, √ is approxi-

mately equals to , then equation (6) becomes

2

(7)

The physical situation has axial symmetry about the -axis.

Hence must have the same magnitude at all points on a

circle centered on the conductor and lying in a plane perpen-

dicular it, and the direction of must be everywhere tangent

to a circle. Thus, at all points on a circle of radius around

the conductor, the magnitude is

2

(8)

Fig. 3 Magnetic field produced by a straight current-carrying conductor of length 2 .


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4. Magnetic Field of a Circular Current Loop

We can use the equation (5) to find the magnetic field at a

point on the axis of the loop, at a distance from the cen-

ter. As Fig. 4 shows, and are perpendicular, and the

direction of the field caused by this particular element

lies in the -plane. Since , the magnitude

of the field due to element is

4

(9)

The total field at has only an -component.

cos4

⁄ (10)

4

⁄ 4 ⁄ (11)

The integral of is just the circumference of the circle,

2 , we finally get

2 ⁄ (12)

The maximum value of the field is at 0, the center of the

loop

2

(13)

Fig. 4 Magnetic field on the axis of circular loop. The current

in the segment causes the field , which lies in the -plane. The currents in other ’s cause ’s with different components perpendicular to the -axis; these components add to zero. The -components of the ’s combine to give the total field at point .

5. Magnetic Field of a Solenoid

Ampere’s law can be used to find the field of an infinitely

long solenoid with turns per unit length carrying a current

. For the integration path as shown in Fig. 5, Ampere’s law

gives ∮ ⋅ , or

(14)

This result demonstrates that the field is uniform over the

entire cross section inside the solenoid. However, the field of

a solenoid with finite length is no longer uniform, so we can’t

use Ampere’s law.

To calculate the magnetic field at a point on the axis of

the solenoid with length as in Fig. 6, integrate Eq. (12)

over all the each single loops, and we finally get

12 √

or12

cos cos

(15)

If the solenoid is infinitely long, or cos cos 1, then

equations (15) become equivalent to equation (14).

Fig. 5 Magnetic field produced by the current in a solenoid.

Fig. 6 Magnetic field at point along the axis of a solenoid.


Lab Manual




1. List

Item(s) Qty. Description

PC / Capstone software

1 Records, displays and analyzes the data measured by

sensors.

Interface

1

Data acquisition interface designed for use with various

sensors, including power supplies which provide up to

15 watts of power.

Magnetic Field Sensor

(DIN extension cable included)

1 set Measures the magnitude of magnetic field.

Rotary Motion Sensor

1

Measures angles, angular velocities, etc. of a rotational

motion, and using additional accessories, measures

position, velocities. etc. of a linear motion.

Power Supply

(Power cable included)

1 Supplies DC power up to 30V10A.

A-shaped Base

1 Provides stable support for experiment set-ups.

Support Rod 300mm


Rack

1

Converts a linear motion to a rotational motion in com-

bination with the pinion gear inside the Rotary Motion

Sensor.

Clamp

1 Attaches the Magnetic Sensor to the Rack.

Equipment


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Item(s) Qty. Description

Conductor Adapter

1 Supports circular conductors.

Straight Conductor

1 Thickness: 4mm

Circular Conductors

1 set Radii: 0.03m, 0.04m

Conductor Bases


Solenoid

1

Length: 0.13m

Radius: 0.0195m

Turns: 2900

Patch Cords

(with banana plugs)

2 Carry the electric current.

2. Details

(1) Power supply

This power supply provides DC power up to 30V10A. It can

be operated in either of the two modes: CC (constant current)

and CV (constant voltage) mode, which are indicated at the

front panel. When the CV lamp is on, it means that the volt-

age you see on the display (which is always the actual volt-

age the power supply is putting on) is the same as the volt-

age you set, while the current you set is higher than the set

by the voltage adjustment knob. Alternatively, when the CC

lamp is on, the current on the display (which always shows

the actual current flowing through the circuit) is the same as

the current limit you set, and the voltage limit you set is high-

er than the actual voltage displayed on the power supply.


Lab Manual




(2) Rotary Motion Sensor

The Rotary Motion Sensor is a bidirectional angle sensor

designed to measure rotational or linear position, velocity

and acceleration.

Inside the sensor, there are a small photogate sensor and

an optical code wheel on which dark bands are printed in line.

As the shaft of the sensor rotates, the bands block the infra-

red beam of the photogate, which provides very accurate

signals for positioning or timing.

A rack can be inserted into the T-slot in the side of the sen-

sor. The gear teeth on the rack mesh with the gear teeth on

the pinion gear inside the senor. This allows you to convert a

linear motion into a rotational motion.

(3) Magnetic Field Sensor

The magnetic Field Sensor measures a vector component

of the magnetic field near the sensor probe.

[RADIAL] measures transverse magnetic field.

[AXIAL] measures longitudinal magnetic field.

[TARE] sets the output of the sensor at zero.

[1X] - range 0.1T (resolution 5 10 T)

[10X] – range 0.01T (resolution 5 10 T)

[100X] – range 0.001T (resolution 5 10 T)

The sensor uses Hall Effect devices as sensing elements.

When a magnetic field present, charge carriers in a conduc-

tor strip, as shown below, experience a force and their paths

are curved so that moving charges accumulate on one face

of the conductor. The separation of charges establishes an

electric field and this field causes a transverse potential dif-

ference between opposite edges of the conductor strip. This

is called the Hall Effect.

There are two of these devices oriented perpendicularly to

one another located at the end of the probe. One is sensitive

to axial field lines that are parallel to the length of the probe

and the other is sensitive to radial field lines that are perpen-

dicular to the probe. A small white dot on the probe end indi-

cates the plane of each sensing device.


Lab Manual




Experiment 1. Magnetic Field

of a Straight Current-Carrying Conductor

(1) Set up your equipment.

Attach the Magnetic Field Sensor to one end of the Rack

using the clamp. Insert the other end of the Rack to T-slot on

the side of the Rotary Motion Sensor. (The teeth on the Rack

go through the T-slot and then engage a pinion gear that is on

the shaft of the sensor.)

(2) Set up the PASCO Capstone software.

① Run PASCO Capstone.

② Add the Rotary Motion Sensor.

Click [Hardware Setup] in the [Tools] palette. Confirm the

panel shows the icon of the Rotary Motion Sensor. (In gen-

eral, the interface automatically recognizes the Rotary Motion

Sensor.)

If the sensor is not in the panel, click the input port which

you plugged the sensor into. A drop down menu of sensors

will appear. Select [Rotary Motion Sensor] from the list and

the sensor’s icon will be added to the panel.

Procedure


Lab Manual




③ Add the Magnetic Field Sensor.

Click the input port which you plugged the sensor into and

select [Magnetic Field Sensor] from the list.

④ Configure the Rotary Motion Sensor.

Click the Rotary Motion Sensor icon in the [Hardware Setup]

panel and then click the properties button (☼) in the lower

right corner.

In the [Properties] window, select [Rack & Pinion] for [Linear

Accessory].

[Change Sign] switches the sign on the sensor. The sign of

collected data depends on the setup status or rotational di-

rection of the sensor shaft. Activate [Change Sign] if required.

Confirm [Zero Sensor Measurements at Start] is activated.

⑤ Create a graph.

Click and drag the [Graph] icon from the [Displays] palette

into the workbook page.

A graph display will appear.


Lab Manual




⑥ Configure the -axis of the graph.

Set up the graph display to show the position of a measuring

point on the -axis.

Click <Select Measurement> on the vertical axis and pick

[Rotary Motion Sensor] [Position(m)] from the menu.

⑦ Configure the -axis of the graph.

Set up the graph display to show the magnitude of magnetic

field on the -axis.

Click <Select Measurement> on the horizontal axis and pick

[Magnetic Field Sensor] [Magnetic Field Strength (100X)(T)]

from the menu.

(3) Set the magnetic field sensor.

Orientation : [RADIAL]

Range : [100X] 10 T

[TARE] button is for zeroing the sensor.

(4) Supply 5A to the conductor.

Before turning on the power supply, rotate the voltage and

current adjustment knobs fully counterclockwise for no output

settings.

Turn on the power supply and rotate the voltage adjustment

knob fully clockwise. Then set the current through the con-

ductor at 5A by using the current adjustment knob.

Note

If you cannot obtain the desired output current:

① Check the connections. Make sure the power supply

is properly connected to the conductor.

② Check if the CV lamp is on. It indicates that the DC

output is in constant voltage mode, i.e. the voltage level

you set is too low. Increase the voltage level by rotating

the voltage adjustment knob clockwise.


Lab Manual




(5) Begin collecting data.

Click the [Record] button at the left end of the [Controls]

palette to begin collecting data.

Let the end of the probe touch the conductor (the white dot

side of the probe must face up), and then slowly move the

sensor away from the conductor, until the end of the probe is

separated about 15cm from the conductor.

(6) End the data collection.

Click the [Stop] button to end the data collection.

(7) Scale the graph.

Adjust the scale of the graph automatically by clicking [Scale

axes…] icon in the toolbar.

Note

Prior to any measurement, place the Magnetic Field

Sensor away from any magnetic sources (current carry-

ing conductor, power cables, and even your smartphone)

and then press the TARE button on top of the sensor.

Pressing the TARE zeroes the sensor at the value of the

field it is reading at the moment the button pressed. That

means your measurement of the field is not an absolute

measurement, but a relative measurement (relative to the

value of the field when you press the TARE button).

Therefore, pressing the TARE under the influence of any

magnetic field might cause spurious results of the exper-

iment.

For the best result, you should zero the sensor frequent-

ly, every time before each measurement.

Note

You can also scale or pan the graph manually.


Lab Manual




(8) Analyze the graph.

Click [Show coordinates…] to read off data points.

If you want to see more precise values of the collected data,

you can use a table display. Drag the [Table] icon into the

workbook page, select appropriate measurements for each

column, and then increase the number of digits by using the

tool-bar icon as shown below.

Note

You may get a noisy curve due to the influence of exter-

nal magnetic fields, unstable signal of the sensor, or your

measurement skills. [Curve Fitting] can be used to find a

smooth function that approximately fits the data.

(Continued)

① Click [Select range …] in the toolbar and select a re-

gion of interest by resizing the rectangle. (Selected data

is highlighted in yellow.)

② Click [▼] of [Select curve fits …] and select the curve

fit that you wish to apply to the selected data.

③ The fit function of the data will appear.


Lab Manual




(9) Record your data.

Find the values of magnetic field on the graph at the dis-

tance 0.01, 0.02, 0.03, 0.04, 0.05m.

(10) Repeat your experiment.

Repeat the steps (5)-(9) more than 5 times.

(11) Analyze your results.

2

(8)

m 0.01 0.02 0.03 0.04 0.05

T

1st

2nd

3rd

4th

5th

2⁄

Experiment 2. Magnetic Field

of a Circular Current Loop

(1) Set up the equipment.

Mount the circular conductor of radius 0.03m on the

base using the Conductor Adapter.

(2) Set the Magnetic Field Sensor.

Orientation : [AXIAL]

Range : [100X] ( 10 T

(3) Supply 5A to the conductor.

Note

The measured value at 0 on the graph is NOT the

magnetic field strength at 0 of 2⁄ .

The Hall sensor in the probe is at 8.5mm distance from

the center of the conductor when the probe touches the

conductor.

This means that the value at 0 on the graph is the

magnetic field strength at 8.5mm distance from the

center of the conductor.


Lab Manual





Slowly move the sensor along the axis of the circular con-

ductor, keeping the probe parallel to the axis.


Note

Prior to any measurement, place the Magnetic Field

Sensor away from any magnetic sources, and then press

the TARE button on top of the sensor. For the best result,

you should zero the sensor frequently, every time before

each measurement.

Note

As already explained in previous experiment, [Curve

Fitting] can be used to find a smooth function of your

data.

① Select [User Defined: f(x)].

② Click the curve fit legend.

③ [Curve Fit Editor] appears in the [Tools] palette.


Lab Manual




(6) Record your data.

Find the values of magnetic field on the graph at the

point 0.00, 0.01, 0.02, 0.03, 0.04m. (The maximum value

of the graph is the field strength of the conductor center.)

(7) Repeat your experiment.

Repeat the steps (4)-(5) more than 5 times.

2 ⁄ (12)

m 0.00 0.01 0.02 0.03 0.04

T

1st

2nd

3rd

4th

5th

(8) Repeat the experiment using the circular conductor of

radius 0.04m.

2 ⁄ → ⁄

④ Enter your function and click [Apply].

→ y=A*a^2/((x-x0)^2+a^2)^(3/2)+y0

The fit function may not appear at the very moment.

In this case, you need to enter the values in the [Initial

Guess] boxes to modify the function.

1) Click [Lock] check box next to the radius 0.03m

to lock this entry. 2) Enter , 0.06, 0 , since the

fit is shifted to the right about 0.06, 0

from , as shown the graph above. (It depends on

your data.). 3) You can also enter the calculated value

of A /2. (You don’t have to enter all initial guesses.)

4) Click [Update Fit].

⑤ The fit function of the data will appear.


Lab Manual




Experiment 3. Magnetic field of a solenoid

(1) Set up the equipment.

We will use the built-in power supply of the interface.

(2) Set up the data acquisition software.

① Add sensors.

Add the Rotary Motion Sensor and the Magnetic Field Sen-

sor as explained in previous experiments. In addition, add

[Output Voltage Current Sensor] by clicking the output port

which you connected the solenoid to.

② Configure a current output.

Click [Signal Generator] in the [Tools] palette and select [850

Output 1].

[Waveform] : DC

[DC Voltage] : 10V

[Auto] automatically starts/stops the signal generator when

the interface starts/stops recording data.

③ Create a graph.

-axis : [Position(m)]

-axis : [Magnetic Field Strength (10X) (T)]

④ Create a digital meter.

Create a digital meter to measure the current through the

solenoid. Drag the [Digits] icon from the [Displays] palette into

the workbook page, and select [Output Current (A)] for the

measurement.


Lab Manual




(3) Set the Magnetic Field Sensor.

Orientation : [AXIAL]

Range : [10X] ( 10 T

[TARE] button is used to zero the sensor


Put the sensor inside the solenoid and measure the magnet-

ic field all over the inside and outside of the solenoid, keeping

the sensor probe parallel to the axis of the solenoid.


Read the current through the solenoid from the digital meter.

If the graph shows the values of magnetic field as zero, you

can see precise values using a table display. Drag the [Table]

icon display into the workbook page, select measurements

for each column, and then increase the number of digits by

using the icon as shown below.

(6) Record and analyze your results.

Repeat the steps (4)-(5) more than 5 times and find the val-

ues of magnetic field at the center and edge of the sole-

noid. (See note of the next page.)

12 √

(15)

center end

T

1st

2nd

3rd

4th

5th


Lab Manual




12 √

→ A

Note

Use [Curve Fitting] to find the values of magnetic field at

center or at edge of the solenoid.

Enter your function and click [Apply].

→ y=A*((x-x0)/((x-x0)^2+a^2)^(1/2)+

(0.13-(x-x0))/((0.13-(x-x0))^2+a^2)^(1/2))+y0

Click [Lock] check box next to the radius 0.0195m

to lock this entry.

Enter the calculated value of A /2 if required.

(Continued)

The origin of is on the point O (left end of the so-

lenoid) as shown below.

If you insert the sensor into the right side of the sole-

noid, the measuring point of the probe may reach near

the center 0.130/2 0.065m of the solenoid. Thus,

the fit is shifted about 0.065, 0 from

.

Enter the initial guesses , 0.065, 0 and

Click [Update Fit].

The fit function of the data will appear.

The fit value 0.0692 shows that the point O (left

end of the solenoid) is on 0.0692 of the graph.

(This depends on your result.) Since the length of the

solenoid is 0.130m, the center of the solenoid is on

0.0692 0.0650 0.0042 and the right

edge of the solenoid is on 0.0692 0.130

0.0608 of the graph.


Lab Manual




Your TA will inform you of the guidelines for writing the laboratory report during the lecture.

Please put your equipment in order as shown below.

□ Delete your data files and empty the trash can from the lab computer.

□ Turn off the Computer and the Interface.

□ With the voltage and current adjustment knobs set at zero, turn off the power supply and unplug the power cable.

□ Handle the solenoid carefully to avoid scratching or stabbing the coils.

□ Do not disassemble the Magnetic Field Sensor assembly.

Result & Discussion

End of Lab Checklist

000 Bfield ENG rev5 20160901 - Yonsei Universityphylab.yonsei.ac.kr/exp_ref/205_Bfield_ENG.pdf ·...

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