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Recently Asked Statics Questions

Expert help when you need it

Q1:Problem 5: Obtain the electric field at point (x, 0, 0) for the line {x = 0, y = 0, 2 € [0, L]} carrying a nonuniform line charge pr(2) = P. (1- 2). Problem 6: Obtain the electric field at point (0,0, 2) for a the curve {p = a, o € [0, 7], z = 0} carrying a uniform line charge pr.See Answer
Q2:I. A toroid of Material M (BCC, a = 0.425 nm) has an inner diameter of 14 cm, outer diameter of 25 cm, and height of 0.2 cm. The toroid is wrapped by a copper wire in 14 turns. You can assume each atom of the Material M is associated with 0.65 Bohr magnetons. a. What is the saturation magnetization of M? b. If a current of 43 A is flowing in the winding, what are the magnetic fields (in A/ m) in the toroid at its outer and inner diameter, respectively? c. If the relative magnetic permeability of the toroid material is 71, what are the magnetic flux densities (in T) at its outer and inner diameter, respectively? d. Estimate the inductance (in uH) of the toroid inductor. II. A dielectric material is sandwiched between two identical metallic plates to form a capacitor. Each plate has an area of 2300 mm2. The separation distance between the two plates is 3.25 mm. a. If the capacitance is 45 pF (1pF = 10-12F), what is the relative permittivity of the dielectric material? b. Calculate the electric susceptibility of the dielectric material. c. If each plate stores an equal and opposite charge of 13-10 C, what is the strength of the electric field in the dielectric?See Answer
Q3:2. Two charges +q are placed at (x, y) = (0, a) and (x, y) = (a,0), where a has units of length. A third charge -2g is placed at (x, y) = (0,0). a. Draw a picture of this charge configuration. b. Find the potential energy stored in this charge configuration. c. Is this potential energy positive or negative?See Answer
Q4:WAC Essay#1 - PHY 244 Provide a brief description of Experiment #1 The Coulomb Balance. In your essay you can also discuss the broader implications of the analysis from this lab. - Your essay should be written in size 11 "Times New Roman" font, double-spaced with 1 inch left and right margins. - Place your name, the date, course name, professor, and TA in the top right corner of the essay. - Your essay must meet the 500-word minimum, headings not included. - Your essay will be checked for plagiarism. If this is detected the penalties specified in the Student Conduct Code will be applied. - Please submit an electronic copy of your essay on Blackboard by the specified deadline. Grading rubric for your essay: Possible Points Essay 1. Describe the goals of the experiment. 2. Concepts behind the experiment. 3. History & importance of the phenomena illustrated, or physical quantity measured. 4. Organization & Structure 5. Clarity of Expression 6. References - Minimum of three, MLA format. 7. Punctuality Essay Score 100 IF ESSAY IS NOT ACCEPTED: REVISE AND BE SURE TO INCLUDE THE ORIGINAL ESSAY AND SCORING RUBRIC WITH THE REVISION. REVISION DUE: In order to pass the WAC requirements, your essay score must be 70% or greater. 5 15 20 20 20 10 Your Score 10 PLEASE UTILIZE THE CSU WRITING CENTER. IT IS AVAILABLE TO ALL MEMBERS OF THE CSU COMMUNITY. FURTHER INFORMATION CAN BE FOUND ON THEIR WEBSITE: http://www.csuohio.edu/academic/writingcenter//n I. OBJECTIVES 1. To verify Coulomb's law by measuring the force between two charged spheres as a function of distance. 2. To investigate the effect of systematic errors on measurements. 3. To understand the limitations of modeling real charged systems as point charges II. EQUIPMENT EXPERIMENT 1 The Coulomb Balance - Coulomb Torsion Balance (Figure 1) (model PASCO ES - 9070). As part of the balance, a conductive sphere of radius 1.9 cm is mounted on a rod, counterbalanced, and suspended from a thin torsion wire. An identical sphere is mounted on a slide assembly allowing it to be placed at fixed distances from the equilibrium position of the suspended sphere. The electrostatic force between the spheres causes the torsion wire to twist. The experimenter then twists the torsion wire to bring the balance back to its equilibrium position. The angle through which the torsion wire must be twisted to reestablish equilibrium is directly proportional to the electrostatic force between the spheres. - High Voltage Power supply. This is used to charge the two spheres to the same potential, i.e. same charge since the spheres are identical. The Coulomb Balance |F| = k torsion knob index lines aligned degree scale charged spheres -torsion wire torsion wire retainer Figure 1. Side view of the Coulomb balance. slide assembly Historical Note The Coulomb law was published for the first time by Charles Augustine de Coulomb in 1785. It is also referred as the Coulomb's inverse square law indicating the particular distance dependence of the magnitude of the force F between two point-like charged particles: 9192 R2 (1) where k (~8.987x10⁹ Nm²/C²) is a constant, q, and q2 are the two charge values, and is the distance between the charges. A quick calculation with the charges q, and q2 set to 1 Coulomb would indicate that the force between them would be enormous. Despite this, we need a delicate balance to characterize the Coulomb's force because in reality only small charge differential can be sustained in the laboratory (much smaller than 1 C). The limit on the charge differentials possible is a direct consequence of the strength of this force that prevents the separation of the negative (electrons) and the positive (protons) charges. Page 4 ,copper rings lateral support bar Figure 2. Top view of the Coulomb balance. Page 3 A III. PROCEDURE In the event of high atmospheric humidity, the experiment might be particularly challenging due to the NOTE: possibility for the charges to leak of the spheres before an accurate measurement can be taken. The main goal of this lab is to verify the inverse square law dependence of the force on the separation between the charges. Since we are interested only in the qualitative behavior, we do not need to actually calculate the force. Thus we will not measure the charges placed on the spheres, but just make sure that they remain the same throughout the experiment by always using the same voltage source to charge the spheres. Also, we will consider that the value of the angle through which the torsion wire has to be twisted to reestablish equilibrium is in effect a measure of the strength of the electrostatic force between the spheres. 1. Preparing your experiment: Make sure that the spheres are fully discharged by touching them with a grounded probe. Move the sliding sphere as far as possible from the suspended sphere. Set the torsion dial to 0°. Zero the torsion balance appropriately by rotating the bottom torsion wire retainer until the pendulum assembly is at its zero displacement position as indicated by the index marks (see Figure 2). 2. With the spheres still at maximum separation, charge both spheres to the same potential ~ 6-7 kV, using the charging probe (one terminal of the power supply should be grounded.) Immediately after charging the spheres, turn the power supply off to avoid high voltage leakage effects. 3. Position the sliding sphere at a distance of 20 cm. The suspended sphere will deflect. Adjust the torsion knob as necessary to balance the forces and bring the pendulum back to zero position. Record the distance (R) and the angle 0 in Table 1 from page 4. 4. Repeat steps 2 and 3 two more times recording the data in the table. NOTE: Sometimes during the experiments you might accidentally touch the spheres or breathe near them adding moisture to the air and thus promoting charge leaking. In these situations the results for the deflection of the suspended sphere will be inconsistent. If such a situation occurs you should discard that particular measurement and repeat it. Typically, with the PASCO balance, measurements taken within the same conditions (same charge and same distance between the spheres) should be around ±1° from each other. 5. Repeat steps 2-4 for separations 14, 10, 9, 8, 7, 6, and 5 cm. IV. DATA ANALYSIS Even without knowing the details of the Coulomb's law, based on the data obtained we can infer that there is a relationship between the force between the spheres (measured by the angle ) and the distance R between them. One general type of relationship that we can consider between the numerical values of 0 and R is: 0= b.Rn (2) where b is onstant (related with the magnitude of the charges of the spheres) and n is an exponent that we would like to determine as it represents the essence of the Coulomb law. If we take the log of both sides of the relationship (2) between the numerical values of and R and using the properties of the log function we obtain: loge = logb + nlogR The Coulomb Balance (3) Page 4 Question 1: If we graph t Slope 1 aken. hallenging due to the tually separation S fu Bal. Question 1: If we graph the loge vs. logR how can we determine the exponent n from the data? Slope of togo vs log R is the Q vs 1. For each distance R calculate the mean of the three angles recorded. 2. Plot the logarithm of the mean angles calculated as a function of the distance R. 3. From the log Oavg vs. logR determine the slope n and the intercept logb. 4. Since n is determined as a slope, use the formula (5) from the "Brief Notes on Measurement and Errors" to calculate its uncertainty. Note that in this particular case in the formula: y, are the values for log Oavg; X, are the values for logR; A = n i.e. the slope; B = logb i.e. the intercept; and N is the number of distances used. -1.64±3.$9357. Question 2: What is the value of n determined? 32 A pot avea Value of n = YOY Question 3: Is this value consistent with the accepted value n = -2 from the Coulomb law? You should justify your answer in terms of the criteria x ±1.96s (see "Brief Notes on Measurement and Errors" page 1-4 for details) Yes it is very is the " nell The Coulomb Balance sitt JOS HITOV SW amo is the Question 4: Chances are that the value obtained is not exactly 2. Provide some ideas of why this is case. (Hints: Look at your graph. Is it really linear? Are we justified to use a linear fitting?) that could close to to-2 corrected [-164]. It is because could occur. errory systematic. One of the major flaws in the above analysis was considering the spheres as point objects. The main assumption is that the distance between the charges involved is equal with the distance between the centers of the spheres. However, as the charges are distributed on the surface of the spheres this is not true. While charge distribution on macroscopic objects is something that you will investigate later in the course, your data can be corrected for this effect by dividing the angles by a correction factor: a³ of various errors Weather, Human error. random C=1-4 where a = 1.9 cm is the radius of the spheres and R is the distance between their centers. 5. Calculate corrected values for your angle using the above correction factor: Javg R3 = wid NS. (5) Page 5 - PRE-LAB Report - Due prior to lab (If you need more pages to answer the questions below, staple them together.) Full Name: Full Title of Experiment: The coulumb 1 Khizar Ismail - Effect of - of 1) 2pts What are the objectives of the lab? -Verify coulumb's Law by measuring spheres! Lab Section: Make sure with the spheres still to the same potential we 2 systematic errors on Understand the limitations. Of modeling reat charg c 2) 4pts Briefly describe the procedure of the laboratory and the equipment/software that will be used. discharge the spheres Positioning the Sliding sphere -suspended sphere will deflect -Repeat steps. The Coulomb Balance Balance force, blu and record dada. measurements log@= log b + nlog R. | Qcorrected = Qaug C. a) man seperation charge both spheres using the chargingen proble arstance of пост. 6-7 kv 3) 4pts Briefly describe the theory, including all relevant equations and calculations. PH00=n4 bekq19/2 R² K₂ 8. 987x 10⁹ Nm²/C² 2 charged → Coulumb law was published by charles Augustine. Q= b.R" C= 1-4 93 R³ systems. Page 2 I. OBJECTIVES The distance. 1. To verify Coulomb 2. To investic 3. To II. E n goal of this lab is to very uic IIVEIoE squale law upcaucuce UI LIE JUIVE UMI uv Depaiauvi charges. Since we are interested only in the qualitative behavior, we do not need to actually force. Thus we will not measure the charges placed on the the same throughout the re been ans that missing avg [1 19.7 34.0 63.7 76.0 95.7 107.7 36.0 !! or An .049 in log(R) (x) 1.30 1.15 1.00 0.95 0.90 0.85 0.78 (y-Ax-B)^2 5.27E-06 3.72E-04 1.64E-04 2.09E-04 9.17E-04 1.90E-04 5.02E-04 Khizar Ismail (y-Ax-B)^2 5.85E-05 4.66E-04 1.60E-05 3.32E-05 5.69E-04 1.84E-04 3.54E-05 log(0avg) (y) 1.29 1.53 1.80 1.88 1.98 2.03 2.13 x^2 1.693 1.314 1.000 0.911 0.816 0.714 0.606 log(R) (x) log(corrected) (y) 1.30 1.30 1.15 1.54 1.00 1.82 0.95 1.90 0.90 2.00 0.85 2.07 0.78 2.19 x^2 1.693 1.314 1.000 0.911 0.816 0.714 0.606 2867688 log theta avg (y) log theta corrected 2.50 2.00 1.50 1.00 0.50 0.00 2.50 2.00 1.50 1.00 0.50 0.00 0.00 0.00 0.20 0.20 log theta(y) vs log R(x) 0.40 0.60 0.40 log R (x) log theta(y) vs log R(x) 0.80 0.60 log R(x) 0.80 y=-1.6446x +3.4357 1.00 1.20 y=-1.7421x 3.5541 1.00 1.20 1.40 140See Answer
Q5:Problem 5: Obtain the electric field at point (x, 0, 0) for the line {z = 0, y = 0, z = [0, L]} carrying a , (₁-²). nonuniform line charge pi(2) = PoSee Answer
Q6:Problem 2 There is a spherical thin shell of radius a. It carries uniform surface charge with a density of p, C/m². 1. Find the electric fields E at locations with distances R from the center of the spherical shell. Find E for points outside the spherical shell and inside the shell. 2. Find the potential V for points outside the spherical shell and inside the shell. (The reference point for V is set at infinity.) Plot V as a function of R.See Answer
Q7:2. Two long, straight, parallel wires are 1.00 m apart, as in the figure. The wire on the left carries a current /₁ = 6.00 A perpendicular to the plane of the paper (either into the page or out of the page). The wire on the right carries a current /₂ into the plane of the paper. S 90° 0.60 m 0.80 m -1.00 m - -0.50 m→ P I₁ = 6.00 A 12 (a) What is the direction of current, if the net field at point P is zero? (b) What is the magnitude of current /₂ if the net field at point P is zero? (c) What is the magnitude of the net field at point S?See Answer
Q8:5. A cylinder with infinite length, relative permittivity of &,, and radius of R is charged with uniform volume charge density of p. Using Gauss' law, derive the electric field, E, and electric flux density, D, inside and outside of the cylinder. Plot the electric field versus distance and discuss boundary conditions. (Points: 15%) 6. A positive point charge Q is at the center of a spherical conducting shell of an inner radius R; and an outer radius Ro. Determine and plot the electric field E as functions of the radial distance R. Note that as the spherical shell is conducting (metal), the electric field in its inside should be zero. Ri (Point: 15%) I+ Conducting shell 7. A sphere is charged with nonuniform charge density of p(r) = Po where po is a constant and "a" is the sphere radius. The material relative permittivity is &. Using Gauss' law, derive the electric field inside and outside of the sphere. (Point: 15%) 8. Summarize the most important concepts and theories you have learned in this chapter in a maximum of one page. (Points: 15%)See Answer
Q9: 1. An electron at point A in the figure has a speed v₁ = VO A B K -10.0 cm- 1.41 × 106 m/s. (a) Find the magnitude and direction of the magnetic field that will cause the electron to follow the semicircular path from point A to point B in the figure. (b) Find the time required for the electron to move from A to B. 2. The circuit in the figure below is located in a magnetic field whose magnitude varies with time according to the expression B = 1.00 × 10-³t, where B is in teslas and t is in seconds. Assume the resistance per length of the wire is 0.105 N/m. (a) Find the current in section PQ of length a = 58.0 cm. (b) What is the direction of the magnetic force on the section PQ? a ******** x * * **** Bin Pin ***** ******** 2a P 0 **** ** **** **** a 2See Answer
Q10:1. An electron at point A in the figure has a speed v₁ = 1.41 × 106 m/s. νο A -10.0 cm- B (a) Find the magnitude and direction of the magnetic field that will cause the electron to follow the semicircular path from point A to point B in the figure. (b) Find the time required for the electron to move from A to B.See Answer
Q11:2. The circuit in the figure below is located in a magnetic field whose magnitude varies with time according to the expression B = 1.00 x 10-³t, where B is in teslas and t is in seconds. Assume the resistance per length of the wire is 0.105 Q/m. (a) Find the current in section PQ of length a = 58.0 cm. (b) What is the direction of the magnetic force on the section PQ? * * ** a * * * * Bin ***** xxxxxxxx 2a P * * * * 07 **** ****See Answer
Q12: 1. A positive point charge q₁ = +2.00 µC is fixed in position at the A center of a square of side a = 10.0 cm, as in the figure. A second point charge q2 is fixed to either corner B, corner C, or corner D. The net electric field at corner A is zero. (a) At which corner is the second charge located? (b) Is the second charge positive or negative? (c) What is the magnitude of this second charge? (d) What is the electric potential at corner A? A third charge qo = +3.00 µC is now placed at corner A of the square. (e) What is the net force exerted on this charge? (f) What is the potential energy of charge qo? (g) What is the potential energy of the system of three charges? D +9₁ 2 B C aSee Answer
Q13:6. A positive point charge Q is at the center of a spherical conducting shell of an inner radius R; and an outer radius Ro. Determine and plot the electric field E as functions of the radial distance R. Note that as the spherical shell is conducting (metal), the electric field in its inside should be zero. (Point: 15%) R₁ Conducting shellSee Answer
Q14:4. [-/1 Points] DETAILS SERPSE10 23.2.OP.007. ASK YOUR TEACHER PRACTICE ANOTHER Consider a closed triangular box resting within a horizontal electric field of magnitude E= 8.32 x 104 N/C as shown in the figure below. MY NOTES 10.0 cm (a) Calculate the electric flux through the vertical rectangular surface of the box. kNm²/C 30.0 cm 60.0⁰ (b) Calculate the electric flux through the slanted surface of the box. kNm²/C Need Help? (c) Calculate the electric flux through the entire surface of the box. kN-m²/C Submit Answer Read It Watch ItSee Answer
Q15: A camshaft rotates 650 rpm, causing a follower to raise and lower once per revolution. The follower is to be held against the cam by a helical compression spring with a force that varies between Fmin = 300 and Fmax = 600 N as the spring length varies over a range of AL = 25 mm. Ends are to be squared and ground. The material is chrome-vanadium ASTM A232, with Young's modulus E = 203 GPa and shear modulus G = 77 GPa. The wire diameter to be used is d = 6 mm. S sa + Se se S. sm Sa su =1, Homework 2 MAE 156A - Winter 2024 Cam Squared and ground ends, ASTM A232 spring wire n = 650 rpm I Key A + 25 a) Determine the spring rate k. b) Estimate the ultimate tensile strength Sut for the spring material using Table 10-4 at the end of the document. Also estimate the endurance limit as Se≈ Sut/2. Finally, calculate the ultimate shear strength as S = S/√√3 and the shear endurance limit as S = S/√√3 (according to von Mises criterion). su se c) Using Goodman's rule for shear stress, 600 N 600 N Shaft 300 N 300 N 25 mm allow Ssm determine the maximum allowable midrange shear stress as t m where Ssm is the midrange shear strength component, Ssa is the shear strength amplitude, and n is the safety factor. Use n = 1.2. n 2 Hint: Observe that Ssa/Ssm = Fa/Fm, where Fa = Fmax – Fmin and Fm = (Fmax + Fmin)/2 are the amplitude and midrange of the cyclic loading. allow d) Determine the coil diameter D so that m <T. m Hint: Recall the expression t = Kw where λ = a Lo D 8FD πd3 9 constants. If 2 D correction factor and c = - is the spring index. d e) Determine the number of total coils Nt of the spring. Gd4 Hint: Recall that k = 8ND³ squared and grounded ends, N₁ = N + 2 (not required to be a whole number). 2² where Kw f) Determine the free length of the spring Lo so that the force to solid compression is Fs = 1.1Fmax. Hint: The solid length can be expressed as Ls = Ntd. g) Check whether the spring will buckle, assuming pivoted spring ends (a = 1). Hint: Critical buckling deflection is given by Yer = LoC₁ where N is the number of active coils. For a spring with is the slenderness ratio and C= > >1, the spring is absolutely stable. f₁ = 4c-1 0.615 4c-4 с = 1 Ik 2 Vm + C₂ E 2(E-G)' 9 is the Wahl stress C₂ = h) Compare the loading frequency with the natural frequency of the spring to assess the possibility of resonance (spring surge). Assume the mass density of the spring is p = 7.8 g/cm³. Hint: The natural frequency of the spring is given by 2π² (E-G) 2G+E are elastic where m pV is the mass and V is the wire volume (assume small pitch so that V = Al, where A is the cross section of the wire and / its length). Table 10-4 Constants A and m of Sut = A/dm for Estimating Minimum Tensile Strength of Common Spring Wires Source: From Design Handbook, 1987, p. 19. Courtesy of Associated Spring. Material Music wire* OQ&T wire* Hard-drawn wire Chrome-vanadium wire Chrome-silicon wirel 302 Stainless wire* ASTM No. A228 A229 A227 A232 A401 A313 Phosphor-bronze wire** B159 Exponent m 0.145 0.187 0.190 0.168 0.108 0.146 0.263 0.478 0 0.028 0.064 Diameter, in 0.004-0.256 0.020-0.500 0.028-0.500 0.032-0.437 0.063-0.375 0.013-0.10 0.10-0.20 0.20-0.40 0.004-0.022 0.022-0.075 0.075-0.30 A, kpsi - in™ 201 147 140 169 202 169 128 90 145 121 110 Diameter, mm 0.10-6.5 0.5-12.7 0.7-12.7 0.8-11.1 1.6-9.5 0.3-2.5 2.5-5 5-10 0.1-0.6 0.6-2 2-7.5 A, MPa.mm 2211 1855 1783 2005 1974 1867 2065 2911 1000 913 932 Relative Cost of Wire 2.6 1.3 1.0 3.1 4.0 7.6-11 8.0See Answer
Q16:1. Section 4.1.3 of Griffiths contains a discussion of the electric field acting on a polar molecule. For simplicity, let's assume that a polar molecule can be approximated by a dipole moment p. Compare two cases: a) A polar molecule with dipole moment p in the homogeneous electric field E. b) A polar molecule with dipole moment p in an inhomogeneous electric field (electric field varies in space) E. Derive the force acting on this molecule in both cases. 2. Imagine that you have a high-quality homogeneous isotropic linear dielectric (HfO₂) with dielectric constant &r= 25. Using the solution of Example 4.7 of Griffiths calculate the change of electric field inside the sphere made of such HfO₂ that is put in external homogeneous electric field Eo. Note that there is no free charge placed on the sphere. 3. For the same dielectric as in the previous example (HfO₂ with dielectric constant &, = 25), imagine that a fixed free charge density pf is placed inside such dielectric. Derive the relationship between bound and free charge density inside such dielectric. 4. Calculate the bound charge density p, inside the material with constant polarization P.See Answer
Q17:5. A piece of semiconductor with band gap energy of Eg = 1.0 eV, is illuminated uniformly by light with photon energy of 2.0 eV. If minority electron lifetime t = 0.1 ms. a) Find the rate of excess charge carrier generation (gop) that is required to generate 10¹0/cm³ excess electron. b) What optical power per cm³ is required to generate carrier concentration of 10¹%/cm³. c) Draw the band diagram and define the processes of 1) excitation, 2) radiation less decay, and 3) recombination.See Answer
Q18:4. Find the hole concentration and hole mobility of a p-type semiconductor bar. The Hall measurements is performed, and the following parameters are measured. Hall voltage = 3.0 mV Intensity of magnetic field, B = 10-4 Webber/cm² Sample dimensions: Thickness, 2x10-³ cm, Width, 5x10-2 cm, Length, 2x10-4 cm. When applied a 2x10-4V a current of 3x10-³A was observed across the sample.See Answer
Q19:3. Suppose we have a piece of semiconductor with 5.104 cm length, and doping level of 10¹5/cm³. a) If we apply a 2.5V across the sample, find the current density through the sample. b) If we apply 2500V across the sample, find the current density, assume this is the condition of electron velocity saturation.See Answer
Q20:2. A silicon dopped with 10¹7/cm³ Boron, a) Find its total conductivity and b) Plot its band diagram.See Answer

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