Physics Lab - Surface Tension & Electric Field Strength PDF

# Surface Tension σ = p - r/2 here r - is the radius of capillary. Substitute p for its equivalent pxgXH, σ = p - g - H - r/2 Calculate σ. * In analogous way determine σ for different alcohol concentrations. * Plot the graph of σ as a function of alcohol concentration. ## Electric Field Streng...

# Surface Tension σ = p - r/2 here r - is the radius of capillary. Substitute p for its equivalent pxgXH, σ = p - g - H - r/2 Calculate σ. * In analogous way determine σ for different alcohol concentrations. * Plot the graph of σ as a function of alcohol concentration. ## Electric Field Strength Electric field strength can be expressed as the ratio of potential difference to the respective distance dr E = -do/dr (1.5) where do/dr is the gradient of a potential. It characterizes the charge of potential magnitude along the electric field lines. Sign minus shows that field strength direction coincides with that of the decrease of potential. In a vectorial form (1.5) can be written as E = -grado (1.5) i.e. electric field strength is the gradient of a potential with minus sign. ## Dipole **Theory.** An electric field at any point is defined by two characteristics. One of them is the electric field strength E = F/q (1.1) which is the ratio of the net electric force F, acting on a test charge at that point, to the magnitude q of the test charge. Fields, set up by many sources, superimpose each other, forming a single net field. The vector, specifying the magnitude of the net field at any point, is simply the vector sum of the values of the fields due to each individual source. Taking into account Coulomb's law and Equation (1.1) E of a point charge q can be expressed as a function of the distance r E = k - q/(e - r²) where k = 1/(4 - πε), - permittivity constant. (1.2) Potential Φ is another characteristic of an electric field at a given point. It shows the work W, performed to take charge q from infinity to a given point Φ = W/q The potential of a point charge q Φ = k - q/(cr) (1.3) (1.4) A dipole consists of two charges of equal magnitude but of opposite signs that are held at a fixed distance apart and make up a single unit. Many molecules can be regarded as dipoles, so that our familiarity with the electric field of a dipole helps us to understand interactions among molecules and some other important phenomena, particulary the origin of electrograms in living organisms. The product of either of the charges and their separation constitues the dipole moment (Fig. 1) | | |---|---| | b+ | | | | b- | | | |Fig. 1 | p = q . 1 (1.6) 'p is a vector quantity pointing from the negative charge toward the positive charge. Its units are Cxm. Some molecules exhibit charge separation and therefore have dipole moment. Electrons in water molecule spend most of their time in the vicinity of oxy giving the molecule an electric dipole moment (Fig. 2). | | |---|---| | Fig. 2 | Random fluctuations in the configuration of a molecule can lead to charge separation so the molecule temporally develops a dipole moment. This dipole moment gives rise to an electric field, that in turn leads to charge separation in nearby molecules, giving them dipole moment as well. These are called induced dipoles. In other words an electric field can give rise to the dipole. | | |---|---| | Fig. 3 | The potential of the dipole electric field at a point separated from it of a distance r apart (Fig. 3) Φ = k - p - cos0/(er²) (1.7) where θ is the angle betwen the dipole axis and the line separating the given point. At great distances from the dipole (r>>1) dipole electric field strength is E = k - p - cose/(ε - Γ') (1.8) Dipole as a model is useful in biomedical description of electric fields, generated by single cells, and electrograms. ## Appliances * A plate filled with wet sand, * a galvanometer, * DC source, * two point like electrodes. ## The Principle of Method DC source is the origin of an electric field. Electric charges flow along the lines of electric field, thus, the charge trace coincides with electric field lines. They point from positive pole to negative. Between two separated points in the sand bath constant potential difference Δφ exists which can be evaluated by a galvanometer. If Δφ is of zero magnitude, no current is detected. ## Procedure 1. The sand in a plate is moistened (not too much), then the surface is smoothed and pressed. 2. Connect DC to the poles L, & L₂ (Fig. 4). 3. Divide the line betwen the poles into eight equidistant intervals. 4. Put one arm of the, galvanometer to point 1, another - some distance apart in such a way, that the pointer would be at its initial (zero deflection) place (Δφ is equal to zero). In the same way find other equipotential points. Draw the line joining the points. All these points have the same potential i.e. the line is equipotential. | | |---|---| | Fig. 4 | 5. Repeat the analogous operation for points 2. ..., 7. 6. Calculate the electric field strength between electrodes using the formula Ε = -ΔΦ/Δς (1.9) Δø is estimated by galvanometer. Its arms are put apart for such a separation Δς, that the pointer would deflect no less than 10-20 divisions. One division value is 10-7 A. Δø = IR (1.10) where R = 106 ohms (resistance of the galvanometer). Measure s and using formula (1.9) define E. 7. Following the scale draw equipotential & electric field lines. # Measuring Resistivity ## Goal To measure electrolyte resistivity. ## Theory A substance that conducts electricity in solution or in the fused state because of a presence of ions is called electrolyte. Electrolytic dissociation is the reversible separation of certain substances into oppositely charged ions (anions '-' and cations '+') as a result of solution. For example, sulphuric acid molecules break down totally in water (H₂SO₄ → 2H++SO). Some compounds are only partially dissociated in water. Resistivity (fomerly called specific resistance), symbol p, is the resistance of unit length of the substance with uniform cross section. It is measured in 2-m. Actually it is the resistance of 1 m³. The product of the resistivity and the density is sometimes called the mass resistivity. Resistivity of an electrolyte depends on its concentration, temperature and its type. Resistivity of a living organism is variable from one tissue to another. Tissues containing much liquid are good conductors with low resistivity (electrolytes due to K+, Na+, Cl-, Ca²⁺, Mg²⁺ ions. Those which have low or negligible volume of liquid are of high resistivity. Good conductors are blood, lymph, and spinal liquid. Muscle is of middle conductivity, while bone, dry skin are poor conductors. Tissue conductivity is an important biomedical information to be taken into account in case of electrostimulation of organs and tissues, measuring organism electric current in case of electric hazard situations, ect. AU-shaped glass tube filled with electrolyte and electrodes inserted in it are used for measuring resistivity (Fig. 1). If electrodes are at distance L apart, cross-section area of a glass tube S and electrolyte resistivity is p, then resistance R can be calculated:: R = p·L/S (1) | | |---|---| | Fig. 1 | A Wheatstone's bridge is used to measure R. To avoid polarization of electrodes a. c. source is applied. In case of a. c. source balance position is reached when buzzing diminishes or disappears. It takes place if points Cand D are equipotential (no current between it). Then R = R₁,/1₂ (2) Here R, electrolyte resistance, R - known resistance, 1, 1, length of a wire, T- loudspeaker, Ka. c. source. | | |---|---| | Fig. 2 | ## Procedure 1. Connect the circuit shown in Fig. 2. 2. Place the electrode in a U-shaped tube at definite height MN (Fig.1). 3. Switch on the a. c. source, select R value of such a magnitude that the balance point D were close to midpoint of AB (lowest sound intensity). 4. Take l, and l, readings. 5. Repeat position 4-3 times and take the mean value of l, and l,. Then from Eq. (2) calculate electrolyte R'. 6. Move electrodes upwards (position M, N, in Fig. 1) and in the same way calculate electrolyte resistance R". 7. Calculate R", and R', difference. 8. Take the readings NN and MM and sum up. The sum of NN + MM is length L in m. 9. Take diameter D of internal tube and calculate S S = π·D·D/4 (3) 10. By help of formula (1) calculate the electrolyte resistivity. 11. Fill in the table with the data obtained. | D| L | S | l₁ | R' | R" | ρ | |---|---|---|---|---|---|---| | (m) | (m) | (m²) | (m) | (Ω) | (Ω)| (2·m) | # Thermoresistor **Theory.** It has been shown experimentally, that resistance R of a semiconductor as a function of temperature T can be expressed by formula R = R·exp(ΔE/Κ·T) Here R is a resistance of a semiconductor at great values of temperature, when Κ·T>> ΔΕ, ΔΕ - the activation energy, in the given case the energy of thermal activation, k - Boltzmann's constant (k=8.62·10⁻⁵ eV/K). Taking a logarithm of the equation (1.1) lnR = lnR + ΔΕ/(2·Κ·T) (1.2) In Fig. 1 the value of lnR (ordinate) is plotted as a function to inverse of a temperature 1/T (abscissa). Tangent β tg β = ΔΕ/(2·Κ) = (lnR, - lnR,)/(1/T, - 1/T) (1.3) | | |---|---| | Fig. 1 | From this formula an important physical value ΔE for a given semiconductor can be calculated ΔΕ = 2·Κ·tg β (1.4) ## Procedure 1. Connect the circuit diagram shown in Fig. 2. 2. Put the slider of a reochord to the middle position (a=b). Choose R magnitude in such a way, that ammeter G pointer would be in the middle position (no current, no deflection). In this case R = R. 3. Take the resistance of thermoresistor R, at room temperature. 4. Increasing thermoresistor temperature by heating, take R value for an interval of 20° - 80°C with an increase step on 5º -10°C. 5. Check once more R, for the same values of T, while cooling thermoresistor and take the mean of two values. 6. Fill in the table with the results obtained. Calculate the results you are asked. | T(K) | 1/T(K⁻¹) | R = R (Ω) | lnR | ΔΕ (cV) | |---|---|---|---|---| 7. Plot the graph for lnR = f(1/T). 8. Using the graph lnR=f(1/T) and formula (1.4) calculate AE in eV. | | |---|---| | Fig. 2 | # Measuring Tissue Impedance The tissues of a living organism are of different conductance to an electric current. Some are of high conductance, others are of medial, and some of low conductance. Those of good conductance are organic fluids containing dissolved ions such as blood, spinal liquid, and urine, of medial conductance are internal organs, and muscle tissues, while of low conductance are bones, and dry skin. Living organisms in general have high electric resistance and in this aspect they remind of dielectrics. This is due to the property of living organisms, whose main constituents are polarized dielectric water molecules. Another reason for high resistance is due to the cellular organisation of a tissue. Each cell and its components are surrounded by a biological membrane, composed of a bilipid layer of 7 nm thickness separating intracellular medium from extracellular. Asymmetric ion distribution due to the selective properties of the membrane results in a potential difference across it, thus making a living capacitor with 0.5-1 µF/cm²capacitance.Summarizing, it is possible to say, that high resistance of a living tissue is due to it's capacitance and ohmic resistance. The total opposition to the flow of current | | |---|---| | Fig. 1 | is called an impedance Z. An equivalent electric diagram of living tissue is shown in Fig. 1. Here R, R, - external and internal cell resistances, C membrane capacitance. The tissue impedance value depends upon blood supply and, therefore, it is informative in diagnostic sense. The method is called rheography. Rheograms of different organs and tissues help practical doctors while measuring Z by indirect methods, and appreciating blood flux. While passing through a living tissue, d.c. decreases continuously in a timecourse until it reaches constant magnitude which is much less than its initial value. This is due to the ever increasing e.m.f. of polarisation opposite in sign. The Ohm's law undergoes modification: I = (U-Ep)/R Here I current strength, U voltage applied, R- tissue resistance, Ep - c.m.f. of polarization. For this reason the subthreshold of a.c. of 20-30 kcs/s in reography is applied. ## Principle of the Method If a tissue or part of body is pat accross the a.c. source the current is I = U/Z (1) where U is a voltage, Z - impedance of the tissue or body part. Increase the voltage until you feel current effect. This is a threshold of perception. Then double the voltage and connect the resistor R in line to the tissue. R is adjusted in such a way, that the current in th circuit should be the same. In this case I = 2·U/(R+Z) (2) Taking into account the formulae (1) and (2) we get R = Z (3) Thus, measuring the arm tissue impedance, there is no need to measure U and I, but is enough to know R value. Having measured Z, and Z, for different frequencies f, and f, from impedance formula in parallel connection (Fig. 2) | | |---|---| | Fig. 2 | Z = 1/√1/R² + (2πf₁)²C² (4) Z₂ = 1/√1/R² + (2πf₂)²C² (5) Having solved the equation system (4), and (5) we have RZ, Z₂ -2 C = 1 2πΖΖ₂ ²-² (6) (7) ## Procedure 1. Connect the circuit shown in Fig. 3. 2. Switch on the generator G. 3. Adjust the output voltage at zero value. 4. Set output frequency at 500 c/s. 5. Put rheostat slider position at R=0 ohms. 6. Put two cloths moistened in NaCl solution at 5-10 centimeters separation on the forearm. Then fix metal electrodes P, and P₂. 7. Switch on and off the knob K cach 0.5-1 sec. The person, who is connected to the circuit by help of the voltage handle increases voltage until one feels effect of a current. Note voltmeter readings. 8. Adjust the rheostat at 5000 ohms and after this double the output voltage. 9. Then switching on and off K every 0.5-1 sec. reduce resistance by moving rheostat slider to the left until effect appears. 10. Note rheostat slider position and thus resistance value at this point, which by its magnitude is the same as forearm tissue impedance Z at f =500 c/s. 11. Take measurements of impedance Z at f = 2000 c/s. 12. Using formulae (6) and (7), calculate R and C. 13. Draw conclusions. | | |---|---| | Fig. 3 | # The Oscilloscope **Construction.** The oscilloscope is a device used to produce a visual image of one or a few rapidly varying, low amplitude electrical quantities. The cothode-ray oscilloscope is the most usual type. The use of an oscilloscope enables one to take measurements of duration, amplitude and form of feeble electric oscillations of short duration. For biomedical purposes it is used in a wide range of cases too. All kinds of electrograms (EEG, ECG, ERG, EMG) and biopotentials of single cells can be displayed on the oscilloscope too. The most common block-diagram of an oscilloscope is shown in Fig. 1. | | |---|---| | Fig. 1 | The labels are * Iy input "y" * Ix input "x" * A amplifier "y" * A amplifier "x" * ET- electronic tube * STG sawtooth voltage generator The amplifiers serve for electric signal amplification, if needed, ET to display it on tube screen, STG generates voltage pulses of special form, reminding of a sawtooth Fig. 2. It is worth to note, that sawtooth voltage | | |---|---| | Fig. 2 |