Physics Tangent Galvanometer lab report

Please watch the video of the lab procedure, it is available to watch via the Vimeo link below. 2. Read over the laboratory procedure 3. Fill out the data sheets of the “Tangent galvanometer procedure” document with data from video. 4. Do the calculations to fill out the charts 5. Type a neat, single spaced (12 pt font) 4 page long lab report with the following sections: “Theory/abstract”, “Results”, “Conclusion”, “Questions” from end of lab, respectively. NOTE: I have also included an example report so you may have a specific idea of what the report should look like. There cannot be any plagiarism; my school uses Turn-it-In. No sources or citations, as this is not a requirement Lab 8
The Tangent Galvanometer
Objectives:
• To investigate the induction of a magnetic field by a current-carrying coil.
• To measure the horizontal component of Earth’s magnetic field using a tangent galvanometer.
Equipment:
• Tangent galvanometer with compass
• Rheostat (360
), 12 VDC power supply
• Switch (double-pole, double-throw, DPDT, reversing switch)
• Ammeter (0 − 1.0 A scale)
• Two power leads, four connecting leads
• 30 cm ruler, graph paper
• Demonstration horizontal compass and dip meter
Safety:
• Use the ammeter to monitor the current and the rheostat to limit the current in your circuit.
DO NOT AT ANY TIME ALLOW THE CURRENT TO EXCEED THE MAXIMUM FULL
SCALE CURRENT OF THE AMMETER (1.0 A). This could easily destroy the sensitive
ammeter, melt the coils of the tangent galvanometer, and pose a fire hazard.
8.1 Theory
The magnetic field ~B is measured in the SI unit tesla (T). Other terms that are sometimes used for the
magnetic field are the magnetic induction and the magnetic flux density. A smaller unit, the gauss (G)
is also used. 1 T = 1 × 104 G. Some other quantities in electricity and magnetism and their units are
listed in Appendix F.
87
98
88 LAB 8. THE TANGENT GALVANOMETER
Be
Bc
Br

Figure 8.1: Magnetic field components. All three vectors are in a horizontal plane. Bc is the magnetic field
vector for the field induced by the current-carrying coil, Be is the horizontal component of Earth’s magnetic
field, and Br is the resultant of the two.
When a current travels through a flat circular coil of wire, a magnetic field is induced at the center
of the coil. By the right-hand rule, the direction of this field is perpendicular to the plane of the coil,
and its magnitude is given by
Bc =
μ0 N i
2R
(8.1)
where
Bc is the magnetic field strength (tesla, T) induced by the current-carrying coil,
N is the number of turns in the coil,
μ0 is the permeability of free space, 4π × 10−7 H·m−1or T·m·A−1,
i is the current in the coil (A),
R is the radius of the coil (m).
The magnetic field, that is induced by the current-carrying coil, can be represented by a vector.
The coil may be positioned so that its magnetic field vector is both horizontal and perpendicular to
the horizontal component of Earth’s magnetic field Be (see Fig. 8.1). The total or resultant horizontal
magnetic field vector is the vector resultant Br due to the field Bc of the coil and the horizontal component
Be of the earth. The compass needle will naturally point along this resultant field direction. If there is
no current in the coil, the compass will point approximately north and south, since then Bc is zero. If
there is current in the coil, the compass needle will be deflected away from the north-south line through
an angle θ, as shown in Fig. 8.1. The greater the magnitude of Bc, the greater the angle θ.
From Fig. 8.1, we can see that
tan θ =
Bc
Be
(8.2)
It follows that
Be =
Bc
tan θ
= Bc cot θ (8.3)
There are several simple and convenient ways to measure the horizontal component of Earth’s mag-
netic field. One method is with a “tangent galvanometer”.
The tangent galvanometer, Fig. 8.2 consists of a large, vertically mounted coil that can be tapped
at different points to provide varying numbers of turns N. See Fig. 8.3. At the center of the coil is
99
8.1. THEORY 89
Figure 8.2: The tangent galvanometer.
Figure 8.3: Connections that tap different numbers N of coil turns. For example, connecting to the first terminal
on the left and the third from the left taps 60 coil turns.
100
90 LAB 8. THE TANGENT GALVANOMETER
a horizontally-mounted compass. In this experiment, you will determine the horizontal component of
Earth’s magnetic field with the tangent galvanometer. There are three different methods that can be
used to perform this experiment. Unless your instructor specifies otherwise, we will use the Constant
Current method. Consequently, the instructions that follow are worded with the Constant Current
method in mind.
1. Constant Current
A rheostat is adjusted to maintain the same current, approximately 80-100 mA, and a compass
reading is taken for each number of turns that are connected to the circuit.
2. Constant Deflection
The compass needle is maintained at the same angle of deflection (preferably at 45◦) and the
current is read for each number of turns that are connected to the circuit.
3. Constant Number of Turns
The current is varied for a specified number of turns and simultaneous deflection and current
readings are taken.
In any of the above methods, the best results will be obtained when the compass reading is between
30 and 60 degrees.
WARNING: Use the ammeter to monitor the current and the rheostat to limit the
current in your circuit. DO NOT AT ANY TIME ALLOWTHE CURRENT TO EXCEED
THE MAXIMUM FULL SCALE CURRENT OF THE AMMETER (1.0 A) (the ammeter
is pegged). This could easily destroy the sensitive ammeter, melt the coils of the tangent
galvanometer, and pose a fire hazard.
8.2 Procedure
General cautions for all procedures:
• Have your instructor approve your circuit before you connect it to the electrical power.
• Do not use the 10 turn coil by itself.
• Do not remove the compass from the tangent galvanometer.
• Be very careful not to exceed the maximum full scale current of the ammeter.
1. Remove all materials which may influence the magnetic needle (including the ammeter and rheo-
stat) from the near vicinity of galvanometer.
2. Using the spirit level, adjust the legs of the instrument until it is level.
3. With no current in the coil, the compass needle is lining up along the North-South direction of
Earth’s magnetic field. Envision the plane in which the coil lays. Rotate the apparatus so that
the plane of the coil is in the North-South direction.
The preceding step is very important. To repeat for emphasis, the plane of the
coil must be aligned with the North-South direction of Earth’s magnetic field. Fur-
thermore, the coil of the apparatus must stay in this orientation during the entire
experiment. Take care not to bump it.
101
8.2. PROCEDURE 91
12 VDC G Tangent Galvanometer
A
Ammeter
a b
d e
c
f
g
i i
Figure 8.4: Circuit schematic for this experiment. The DPDT reversing switch (shown at nodes a, b, c, d, e,
and f ) places the tangent galvanometer in series with the rheostat and the ammeter. When the switch is closed
to the left, the current through the tangent galvanometer is in the direction shown. When the switch is closed to
the right, the current direction through the tangent galvanometer is reversed. No connections are made at nodes
c or f. Inside the switch, wires connect node a to node f, as well as node d to node c. The rheostat is shown at
high resistance. Moving the slider to the left gives less resistance. Node g is not connected to the circuit.
4. Without moving the coil, slowly rotate the housing of the compass clockwise so that the aluminum
pointer (which is at right angles to the compass needle) reads N and S, or 0◦and 0◦. This makes
reading the deflections a simple matter, since they will be deflections from 0◦.
5. Open the DPDT reversing switch.
6. Being careful not to bump the tangent galvanometer, connect the circuit as shown in Fig. 8.4,
tapping twenty (20) coil turns for the circuit. Set the rheostat at MAXIMUM resistance.
7. Ask your instructor to approve your circuit. DO NOT CONNECT YOUR CIRCUIT TO
THE ELECTRICAL POWER UNTIL YOUR INSTRUCTOR APPROVES IT.
8. After approval of the circuit by your instructor, connect both power leads to the DC power source
and close the reversing switch. Slowly decrease the resistance of the rheostat until the current i
equals the desired constant amount (between 80 and 100 mA). Record this current in Table 8.1.
Read the compass deflection from each end of the aluminum compass needle and record these
readings as θ1 and θ2, under the column corresponding to N = 20 turns in the coil.
9. Reverse the current with the reversing switch and record the readings from each end of the compass
as θ3 and θ4.
10. Average these four deflections to get ¯θ. Record the mean diameter of the coil that is inscribed on
the tangent galvanometer. With this data, you can calculate Bc and then Be.
11. Repeat this process using other values of N.
12. Examine the demonstration horizontal compass and dip meter. The dip meter is a compass
mounted so that it can rotate in a vertical plane. In the northern hemisphere, the vertical com-
ponent of Earth’s magnetic field causes the dip meter to point downward, while in the southern
hemisphere, the dip meter points upward.
8.2.1 Data
Mean diameter of galvanometer coil, d = 2R:
102
92 LAB 8. THE TANGENT GALVANOMETER
Table 8.1: Data for the Tangent Galvanometer
N 20 30 40 60 70
i (A)
Deflections, One Way
θ1 (◦)
θ2 (◦)
Deflections, Reversed Direction
θ3 (◦)
θ4 (◦)
Calculations
¯θ (◦)
Ni (A)
tan ¯θ
Bc (T)
Be (T)
103
8.3. QUESTIONS 93
Average value of Be:
Compare your value with the known value of the horizontal component of the earth’s magnetic field
in New Orleans: 2.66 × 10−5 T.
8.3 Questions
1. In the experiment, why do we reverse the current and re-measure the deflection angle θ? Why is
θ sometimes different when the current is reversed?
2. If, what we are calculating is the horizontal component of the earth’s magnetic field, what other
component does the earth’s field have? In what direction? What is meant by “angle of dip”? Draw
diagrams to illustrate your points.
3. What are the major sources of error inherent in this experiment?
4. Refer to the table of units in Appendix F and show that a tesla T is equivalent to a weber per
square meter Wb/m2.
5. This experiment measures the horizontal component of the earth’s magnetic field. Devise an
experiment that would determine the earth’s total magnetic field, as well as the angle of dip.
6. On Fig. 8.5 plot a graph of Ni versus tan θ using all of your data. Draw the best fitting straight
line and determine the slope of this line. Use the slope to find Be. Show your calculations. Why
is this statistical treatment of your data superior to the method of averaging Be values that you
used earlier?
104
94 LAB 8. THE TANGENT GALVANOMETER
Figure 8.5: A plot of Ni versus tan θ.
105

Lab 8

The Tangent Galvanometer

PHYS 1034

Sec 004

Zaid Otoum    

2540908

03/12/2019

MD MAHMUDUL HASAN

Theory/ abstract

            In this experiment, the magnetic field is measured from a tangent galvanometer. The circuit schematic for the experiment involved a galvanometer, an ammeter, a rheostat and a power source. The current of every trial of the experiment is 80 mA, which is 0.80 A. the angles of each trial ₁, ₂, ₃^, ₄ are read off the galvanometer. For angles one and two, the two angles should be the same because they are the only different in direction, which goes the same for angles 3 and 4. As table 8.1 in the data section indicates. Then, the average angles for each trial is calculated by adding up the angles and dividing it by 4 (since 4 angles were recorded). The N symbol refers to the number of turns in the coil and the i is the current in the coil (A). When a current travels through a flat circular coil of wire, a magnetic field is induced at the center of the coil. The direction of the field is perpendicular to the plane of the coil, and its magnitude can be calculated by using the equation 8.1 below

Equation 8.1

B_c = (µ₀Ni) / 2R

 

B = magnetic field magnitude (Tesla, T)

= permeability of free space ( )

I = magnitude of the electric current (Amperes, A)

r = the radius of the coil (m)

N = the number of coils

 

B_e is the horizontal component of the earth’s magnetic field and it can be calculated using equation 8.2 below

B_{e =} B_c / tan

the average of the B_e values is taken and is compared to the theoretical value of the horizontal component of the earth which is mentioned down in the data section.

Data:

Note: all data are expressed in the correct SI unit.

Useful unit conversions 1 m = 100 cm

                                         1 A = 1000 mA

Table 8.1 Data for The Tangent galvanometer

N	20	30	40	60	70
i (A)	0.08 A	0.08 A	0.08 A	0.08 A	0.08 A
One way
1 in degrees	15	26	33	43	52
2 in degrees	15	26	33	43	52
3 in degrees	20	27	34	45	42
4 in degrees	20	27	34	45	42
calculations
in degrees	17.5	26.5	33.5	44	47
N i (A)	1.6	2.4	3.2	4.8	5.6
tan	0.315	0.499	0.662	0.996	1.07
BC (T)	9.88*10-6	14.8*10-6	19.8*10-6	29.6*10-6	34.6*10-6
Be (T)	3.14*10-5	2.97*10-5	2.98*10-5	2.98*10-5	3.23*10-5

  ₃ and ₄ are deflections in the reversed direction.

The current on the ammeter reads 80 mA which is 0.08 A for each trial

 The permeability of free space is

The mean diameter of galvanometer coil, d = 2R = 20.35 cm which is 0.2035 m.

The known value of the horizontal component of the earth magnetic field in New Orleans is 2.66 * 10^-5 T.

Calculations

            Table 8.1

The calculations below are for the trail with N = 20, other trials with N = 30, 40, 60 and 70 involves the same exact calculations

The Average angle  = (15+15+20+20) / 4 = 17.5 degrees

N * i = 20 * 0.08 = 1.6 A

Tan  = 0.315

B_c = (µ₀Ni) / 2R = (4π*10^-7*1.6) / 0.2035 = 9.88*10^-6 T

B_e = B_c / tan  = (9.88*10^-6) / 0.315 = 3.14 * 10^-5 T

Average value of B_e = (3.14+2.97+2.98+2.98+3.23) / 5 multiplied by 10^-5 = 3.06* 10^-5 T

Percent error of the experiment.

% error = ((experimental – theoretical) / theoretical) * 100

               = ((3.06*10^-5 – 2.66*10^-5) / 2.66*10^-5 )*100  = 15 %

Results

            As shown in table 8.1 above in the data section, the current is 0.08 A is the same across all trials. The angles for one way deflections for each trial with different number of coils is the same for the two angles because since the circle is 360 degrees, one angle will be in the positive direction and the other will be the complementary same angle in different direction. Same idea applies to angles 3 and 4. By looking at the calculation section in the table above, it can be seen clearly that the greater the angle, the greater the B_c values for each and everyone of the trials. Also, increasing the because the magnitude of B_c is dependent on the current as well as how far the compass pointer traveled (which is the angle). The experimental values of B_e were all close to each other because the angles themselves were close to each other’s value. The average of these B_e values as calculated above (3.06*10^-5) was close enough to the theoretical value of the horizontal component of the earth’s magnetic field in New Orleans, which is 2.66 *10^-5. The percent error was approximately 15%, which is relatively not high. Percentage error was present in the experiment might have been due but not limited to, damages in the wire, air resistance, galvanometer not being completely balance at zero, etc.

Conclusion

            The objectives for this experiment were met. The magnitude (B_c and B_e values ) were calculated and compared to the theoretical value. Overall, experiment went well due to a low percent error of 15%.

 

 

 

Question/ answers

1) In the experiment, why do we reverse the current and re-measure the deflection angle θ? Why is θ sometimes different when the current is reversed?

By reversing the current, the magnitude of the field will be the same but its direction is opposite so it is correct to reverse it.

2) If, what we are calculating is the horizontal component of the earth’s magnetic field, what other component does the earth’s field have? In what direction? What is meant by “angle of dip”? Draw diagrams to illustrate your points.

The magnetic field of the earth have two components, horizontal and vertical. The vertical component is perpendicular to the horizontal component.

Total magnetic field B = √BH2 + BV2

Angle of dip is the angle between the total magnetic field B with the horizontal component BH.

At the pole, the angle of dip = 90°

At the equator, the angle of dip = 0°

 

3) What are the major sources of error inherent to this experiment?

Sources of error include:

1. A) Any of the horizontal or vertical component doesn’t match the standard value.
2. B) Incorrect alignment of the coil.
3. C) Horizontal and vertical component should be positive if any of them is negative, it will affect the results.
4. D) The pointer on the galvanometer is not exactly zero.

4) Refer to the table of units in Appendix F and show that a tesla T is equivalent to a weber per square meter Wb/ m2 .

Magnetic field is measured in tesla (T)

The flux density is wb / m² = 1 T

1 T = 10.000 G

1 T = 1 Wb / m² = 10⁴ G.

5) This experiment measures the horizontal component of the earth’s magnetic field. Devise an experiment that would determine the earth’s total magnetic field, as well as the angle of dip.

Other than Tangent galvanometer, we can use inclinometer experiment by which we can measure angle of dip and the total field.

6) On Fig. 8.5 plot a graph of N i versus tan θ using all of your data. Draw the best fitting straight line and determine the slope of this line. Use the slope to find Be. Show your calculations. Why is this statistical treatment of your data superior to the method pf averaging Be values that you used earlier?