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You are a coach for the Physics Olympics team participating in a competition overseas. You are given the following sample problem to present to your team of students, which you need to solve very quickly: A person is standing on the midline of a soccer field. At one end of the field, as shown in Figure P24.28, is a letter D, consisting of a semicircular metallic ring of radius R and a long straight metal rod of length 2R, the diameter of the ring. The plane of the ring is perpendicular to the ground and perpendicular to the midline of the field shown by the broken line in Figure P24.28. Because of an approaching lightning storm, the semicircular ring and the rod become charged. The ring and the rod each attain a charge Q. What is the electric potential at point P, which is at a position x along the midline of the field, measured from the center of the rod, due to the letter D? Think quickly and use all resources available to you, which include your physics textbook: yon are in competition!
Figure P24.28
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Chapter 24 Solutions
Physics for Scientists and Engineers
- 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_forwarda. Given that D=10xa,cm2 ,determine the flux crossing a 1 m? area that is normal to the axis at x = Зт.arrow_forwardIn a given region of empty space, By = B0 * e-t / T (where B0 and T are constants), but Bx and Bz are constant in time. a. What is the magnitude and direction of the electric curl of that region in terms of B0, T, and time t? b. Assume that Evector always points in the +x direction and is zero at z = 0. Find Ex as a function of position and time. [Hint: the answer is B0 * e-t / T * (z / T) + C] c. Check that the units of your expression make sense.arrow_forward
- Problem 31.31 An electron travels with = 4.00 x 106 m/s through a point in space where E=(2.10 x 105-2.10 x 105) V/m and B = -0.130 T. Part A What is the force on the electron? Express vector F in the form Fz, Fy, where the x and y components in newtons are separated by a comma. F. ΕΧΕΙ ΑΣΦ ? N Submit Request Answer Provide Feedback 12 of 14 He Review Next >arrow_forwardItem 6 A charged object with electric charge q produces an electric field. The SI unit for electric field is N/C, where N is the SI unit for force and C is the SI unit for charge. If at point P there are electric fields from two or more charged objects, then the resultant field is the vector sum of the fields from each object. At point P the electric field E₁ from charge q₁ is 250 N/C in the +y-direction, and the electric field E₂ from charge q2 is 600 N/C in the direction 36.9° from the -y-axis toward the -I-axis. esc ! 1 2 F2 W # 3 80 F3 E $ 4 ▾ PartA 888 F4 R What is the magnitude of the resultant field E=E₁ + E₂ at point P due to these two charges? Express your answer with the appropriate units. Submit Part B 0= Submit O I % X Incorrect; Try Again; 9 attempts remaining 5 HÅ Value Previous Answers Request Answer What is the direction angle of the resultant field E = E₁ + E₂ at point P due to these two charges measured from the +z-axis toward the +y-axis? Express your answer in…arrow_forwardSuppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rp has charge -Q. The electric field E at a radial distance r from the central axis is given by the function: E = ae-T/ao + B/r + bo where alpha (a), beta (8), ao and bo are constants. Find an expression for its capacitance. First, let us derive the potential difference Vah between the two conductors. The potential difference is related to the electric field by: Vab = Edr = - Edr Calculating the antiderivative or indefinite integral, Vab = (-aage-r/a0 + B + bo By definition, the capacitance Cis related to the charge and potential difference by: C = Evaluating with the upper and lower limits of integration for Vab, then simplifying: C= Q/( (e-rb/ao - eTalao) + B In( ) + bo ( ))arrow_forward
- Using the symmetry of the arrangement, determine the direction of the force on +q in the figure below, given that: Case I. qa=qb= +6.5 μC and qc = qd = +6.5 μC. (a) In your notebook, draw the forces on q due to qar qb²9c² (b) Due to symmetry the direction of the net force is F O qc net ✔N O qd Hint: For each force draw the x and y components. Some will add and some will cancel. (c) Calculate the magnitude of the force on the charge q, given that the square is 10.0 cm on a side and q = 2.3 μC. and 9d- Xarrow_forwardInside a vacuum tube, an electron is projected between two parallel Problem 1 plates. The plates are separated by 3 cm and are 10 cm long. Equal but opposite electric charges are placed on the plates, so that there is a uniform electric field between the plates and no field outside of the plates. The electron is projected in the center of the positive plate and its initial velocity is 4.5 x 10 m/s straight towards the center of the negative plate. Find the magnitude of the electric field such that the electron just barely misses touching the negative plate before it turns around goes directly back out of the hole. 10cm. Зстarrow_forwardTwo 16 cm -long thin glass rods uniformly charged to +16nC are placed side by side, 4.0 cm apart. What, are the electric field strengths E₁, E2, and E3 at distances 1.0 cm, 2.0 cm, and 3.0 cm to the right of the rod on the left, along the line connecting the midpoints of the two rods? Part C Specify the electric field strength E3. Express your answer to two significant figures and include the appropriate units. E3 μà -1.2.105 Review | Constants N C S Submit Previous Answers Request Answer Provide Feedback X Incorrect; Try Again; 4 attempts remaining Next >arrow_forward
- Two protons (p) and two electrons (e) are arranged on a circle of radius r = 4 [cm], with angles 0₁ = 20°, 0₂ = 30°, 03 = 20° and 04 = 60°, as shown in the figure. (qp = +1.6 x 10-1⁹ [C] and qe = -1.6 x 10-¹⁹ [C]). The figure is not to scale. a the circle. 04 Ēnet = ( 02 P Find Enet, the net electric field vector produced at the center of ])i + ( [ ]) Ĵ [N/C] b. Where on the circle should a fifth point charge qo be placed (give its angle relative the +x-axis) and what is its value (calculate qo) in order to have Enet (the net electric field at the center of the circle) equals zero (Type the detailed solution to this question in the below box, Show all your calculation steps by typing in the box). X Fiarrow_forwardTwo conductors with concentric radii r1=5 m and r2=23 m are placed in such a way that their center is the origin. While there is a charge Q1=7,1 µC on the circle with radius r1, there is a charge Q2=7,1 µC Accordingly, the electric field at point A(18, 162°, 52°) is given below. Find the amplitude of the electric field. TT=3,1416 E= 36п 10-9 Q2 r2 Q1 A Xarrow_forwardA uranium ion and an iron ion are separated by a distance of ?=60.30 nm.R=60.30 nm. The uranium atom is singly ionized; the iron atom is doubly ionized. Calculate the distance ? from the uranium atom at which an electron will be in equilibrium. Ignore the gravitational attraction between the particles. What is the magnitude of the force on the electron from the uranium ion?arrow_forward
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