Concept explainers
You are still fascinated by the process of inkjet printing, as described in the opening storyline for this chapter. You convince your father to take you to his manufacturing facility to see the machines that print expiration dates on eggs. You strike up a conversation with the technician operating the machine. He tells you that the ink drops are created using a piezoelectric crystal, acoustic waves, and the Plateau–Rayleigh instability, which creates uniform drops of mass m = 1.25 × 10−8 g. While you don’t understand the fancy words, you do recognize mass! The technician also tells you that the drops are charged to a controllable value of q and then projected vertically downward between parallel deflecting plates at a constant terminal speed of 18.5 m/s. The plates are ℓ = 2.25 cm long and have a uniform electric field of magnitude E = 6.35 × 104 N/C between them. Noting your interest in the process, the technician asks you, “If the position on the egg at which the drop is to be deposited requires that its deflection at the bottom end of the plates be 0.17 mm, what is the required charge on the drop?” You quickly get to work to find the answer.
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Chapter 22 Solutions
Physics For Scientists And Engineers
- A Geiger counter is a device used to detect radiation, and consists of a thin metal wire (anode) at the center of a metallic tube (cathode). As radiation enters the tube, electrons are knocked off from the gas inside the tube or from the metallic wall, and accelerate towards the wire at the center. Consider a Geiger counter with an evacuated tube (a vacuum existing between cathode and anode), where the inner anode has a radius 2 mm and the outer cathode has a radius of 44 mm. The anode has a linear charge density of +10 nC/m, while the cathode has a charge per unit length of -10 nC/m. Let the cathode potential be equal to zero (using it as voltage reference). What is the potential at a distance of 73 mm from the center? Express your answer up to four significant figures. Note that this item is synced with the next item and that you can assume that the length of the Geiger counter is much larger than the radius of the cathode. Anode Cathodearrow_forwarda. Use the Cartesian representation L₂ = 1/(x2-17 - 1²/²7) y i ду дх to show that (x + iy)m is an eigenfunction of Îz.arrow_forwardSolve the equations 1/2 mv^2 + 1/2 Iω^2 = mgh and v = rω for the speed v using substitution, given that I = mr^2 and h = 3.76 m. (Note that mass m and radius r will both cancel, so their numerical values aren't required.)arrow_forward
- Scientists in the laboratory create a uniform electric field E-9.0x105 k V/m in a region of space where B = 0. ▼ Part A What are the components of the electric field in the reference frame of a rocket traveling in the positive x-direction at 1.4x108 m/s ? Express your answer using two significant figures separated by commas. Ex, Ey, Ez = 0,0,9.0x105 V/m Submit Previous Answers Correct Part B What are the components of the magnetic field in the reference frame of the rocket? Express your answer using two significant figures separated by commas. VE ΑΣΦ B₂, By, B₂= 0,0, 1.4 10 ● Submit Previous Answers Request Answer X Incorrect; Try Again; One attempt remaining ? Tarrow_forward- D1.2. A vector field S is expressed in rectangular coordinates as S = {125/ [(x - 1)²+(y-2)² + (z+1)²]}{(x − 1)ax +(y− 2)ay+(z+1)a₂}. (a) Evaluate S at P(2, 4, 3). (b) Determine a unit vector that gives the direction of S at P. (c) Specify the surface f(x, y, z) on which |S| = 1. Ans. 5.95ax +11.90ay +23.8az; 0.218ax +0.436ay +0.873az; √(x − 1)² + (y-2)² + (z + 1)² = 125arrow_forwardConsider a simple pendulum with known mass m and unknown length I and charge q. Assume that you can measure time, but charge, cannot. You want to find an expression for q by measuring periods for the cases where electric field E switched off (To) and on (TE). For this purpose, b) Electric field is switched on. Write the electric force on the charge F and find the downward acceleration (a). Do not forget to consider the directions; 1 b) Question 1 part b (second part of question 1) F =qE, a = g + Option 3 F=qE, a = - qE m qE m 'I' (+q Option 1 E F =-qE, a = g F=-qE, a = - (g+ ab) marrow_forwardof the temperature function at the same point in the direction of A mosquito travels in a 3-dimensional space with the velocity field F = (3x² +6y)î –14yzj+20xz°k, in such a way that its position vector is F(1)=ti+t*j+tk. Find the work done by the mosquito to travel from the point (0,0,0) to (1, 1,1). Determine the current in the L-R circuit given in the following figure, if V (t) is an lectromotive force of 30sin(t) Volt, R is a resistor of 102 and L is an inductor of 1 H. Provided the condition that the current is initially zero.arrow_forwardAssume = 36 and H = 4. Determine the x-component of H.arrow_forwardA vector field V is irrotational if ∇ × V = 0. Find constants a, b, c so that V =(−4x−3y+az)i + (bx+3y+5z)j + (4x+cy+3z)k is irrotational. For those values a, b, c, find a function f: R3 → R so that V = ∇f.arrow_forwardIn certain physical models, the nonhomogeneous term, or forcing term, g(t) in the equation ay" + by' + cy = g(t) may not be continuous, but have a jump discontinuity. If this occurs, a reasonable solution can still be obtained using the following procedure. Consider the following initial value problem. 240 if 0sts7T/6 y" + 4y' + 40y = g(t); y(0) = 0, y'(0) = 0, where g(t) = . if t> 7x/6 Complete parts (a) through (c) below. (a) Find a solution to the initial value problem for 0 sts 71/6. The solution for 0sts 7n/6 is y(t) = - 6 e -21 *cos 6t - 2 e - 2t sin 6t + 6 (Type an equation.) (b) Find a general solution for t> 71/6. The general solution for t> 7x/6 is y(t) = C, e-2 cos 6t + C, e -2t sin 6t (Type an equation. Do not use d. D. e, E, i, or I as arbitrary constants since these letters already have defined meanings.) (c) Now choose the constants in the general solution from part (b) so that the solution from part (a) and the solution from part (b) agree, together with their first…arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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