Experiment 1 Introduction To Uncertainty Analysis

Experiment 1 Introduction To Uncertainty Analysis

Topic       : Physical Quantities and Units

Title         : Introduction to Error Analysis

Objective : To estimate the accuracy of  experimental result

Theory    :

Error or uncertainties could be caused by limitation of the measuring instruments, nature of
the measured quantities or other external factors. Error can be classified as systematic error
and random error.

Error analysis is a technique used to determine how error propagates through experimental
procedure. This technique is based on combining the uncertainty for each quantity involved
to estimate the accuracy of  the experimental result.

Propagation of errors: Assume A and B are two measured quantities in an experiment.

1. Addition or Subtraction

If the derived quantity or , then

                                                

2. Multiplication and Division

If the derived quantity or , then

                                            

                                               

The experimental result should be expressed as

The accuracy of the experimental result can be estimated by calculating the percentage error.

                                                                     Percentage error

Apparatus:

(i) A measuring cylinder

                 (ii) A glass rod

                 (iii) A triple beam balance

                 (iv) A micrometre screw gauge

                 (v) A half-metre ruler

Procedure:

Part I: To estimate the error in the determination of density of water.

1. Weigh an empty measuring cylinder.
2. Measure 200 cm3 of water using the measuring cylinder.
3. Weigh the filled measuring cylinder.
4. Calculate the density of water.
5. Estimate the error in your result.

Part II: To estimate the error in the determination of density of glass.

1. Measure the diameter and length of a glass rod.
2. Weigh the glass rod.
3. Calculate the density of the glass rod.
4. Estimate the error in your result.

Data :

Experiment 8 Magnetic Fields

Experiment 8 Magnetic Fields

Topic: Magnetic Fields

Title: Earth's magnetic field

Objective: To estimate the horizontal component of the Earth's magnetic field

Theory:

Figure 11 shows a circular loop of radius R and carry current I situated at distance x from a fixed point P.

Figure 11

The magnetic flux density B at P is

................................(1)

   

whereis the permeability of free space.

Figure 12 shows a solenoid of length L carries current I situated at distance from a fixed point Q.

Figure 12

If the total number of turns in the solenoid is N, then the number of turns dx per  length is . The magnetic field density due these loops can be derive from equation (1) as

...............................(2)

where R is the radius of the solenoid.

Integrating equation (2), the magnetic flux density B due to the solenoid at Q is

Figure 13 shows the magnetic field B from the solenoid and the horizontal component of the Earth's magnetic field acted perpendicular to each other at Q.

From the Figure 13

   

where diameter

Apparatus:

i. Two wooden retort stands and clamps

ii. A cork and an optical pin

iii. A set of small bar magnet fixed with a pair of optical pins

iv. A plane mirror attached to a paper protractor

v. Thread of length about 40 cm

vi. A test-tube wound with copper wires

vii. A 1.5 V dry cell or any other stable power supply

viii. A (0-1A) d.c. ammeter

ix. A switch

x. A rheostat

xi. A pair of vernier calipers

xii. A micrometer screw gauge

xiii. Some connecting wires

Procedure:

a) The cork with a pin is clamped to the retort stand. The bar magnet is hung from the pin using the thread supplied, so that the magnet stays at a height of about 3 cm above the table. The magnet is allowed to stay stationary and horizontal. The mirror is placed with the protractor with the 0° - 180° axis directly below the pins.

b) The solenoid is held by using the other clamp in a horizontal position at the same level with the magnet. The orientation of the solenoid is adjusted so that its axis is perpendicular to the axis of the magnet and one end of the solenoid is at 3.0 cm from the axis of the magnet. A rheostat, ammeter, power supply and switch is connected to the solenoid in series. The ammeter should be kept at least 50 cm from the magnet. The experiment is set up as shown in Figure 14.

c) The rheostat is adjusted to maximum resistance and the switch is then closed. The current I reading  of the ammeter is recorded and the average deflection of the magnet from the 0° - 180° axis is obtained.

d) The value of the resistance of the rheostat is decreased in stages so as to change the value of current I and then the corresponding value of θ is measured.

e) All the measurements for I, θ, and tan θ are recorded.

Figure 14

e) A graph of against I is plotted.

f) The gradient s of the graph of against I is calculated.

g) The solenoid is removed to measure

                   i)The internal diameter D of the solenoid,

                  ii) Average diameter d of the wire used in the solenoid,

                 iii) The length  of the solenoid .

            h) The values of d and are used to estimate the number of turns N in the solenoid.

            i) The value of the horizontal componentBH of the Earth's magnetic field is calculated using the following estimation

Where and

.