Problem 1 [10 points] (a) Calculate the electric potential due to a uniformly charged annulus of inner radius R₁ and outer radius R₂ along the central axis. The surface charge density is o. (b) At distance +x from the disk, still on axis, find the electric field by taking the derivative of the electric potential. (c) Show that you get the same result by considering the potential due to a positively charged disk with charge density +o and radius R₂ with a smaller negatively charged disk with charge density - and radius R₁. This is the principle of superposition. The potential for a charged disk is derived in the textbook. R₂ X R₁ (d) Verify that you will get simple harmonic motion for small displacement near the center, just as for the charged ring. You do not need to do a full calculation- just show the relevant dependence of the field near the origin.

Problem 1 [10 points] (a) Calculate the electric potential due to a uniformly charged annulus of inner radius R₁ and outer radius R₂ along the central axis. The surface charge density is o. (b) At distance +x from the disk, still on axis, find the electric field by taking the derivative of the electric potential. (c) Show that you get the same result by considering the potential due to a positively charged disk with charge density +o and radius R₂ with a smaller negatively charged disk with charge density - and radius R₁. This is the principle of superposition. The potential for a charged disk is derived in the textbook. R₂ X R₁ (d) Verify that you will get simple harmonic motion for small displacement near the center, just as for the charged ring. You do not need to do a full calculation- just show the relevant dependence of the field near the origin.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

I Review | Constants The ammonia molecule (NH3) has a dipole moment of 5.0 x 10-30 C.m. Ammonia molecules in the gas phase are placed in a uniform electric field E with magnitude 1.4x106 N/C. Part A What is the change in electric potential energy when the dipole moment of a molecule changes its orientation with respect to E from parallel to perpendicular? Express your answer using two significant figures. ΑΣφ ? AU = J
Problem 1 Two metal spheres A and B with radii RA and RB rest far away from one another but are connected by a long wire with a switch. With the switch disconnected, only sphere A is charged, with an initial charge Q1. a) What is the initial magnitude of the electric field |E₁| at the surface of sphere A? b) What is the initial electric potential V, at the surface of sphere A, assuming V → 0 an infinite distance away? c) The switch is now connected and the spheres reach electrostatic equilibrium. In terms of the radii, electric constant, and initial charge, what are the final charges QA and QB on each sphere? Assume the wire can transfer charge but only hold a negligible amount. d) What are the final potentials V₁ and VB at the surfaces of each sphere? e) What are the final electric field magnitudes |Ē₁] and |ĒB] at the surfaces of each sphere?
Problem 25.42 Part A A 2.0nC charge is at the origin and a -4.0nC charge is at T = 1,3cm At what a-coordinate could you place a proton so that it would experience no net force? Express your answer to two significant figures and include the appropriate units. HA ? Value Units Submit My Answers Give Up Part B Would the net force be zero for an electron placed at the same position? O Yes O No Submit My Answers Give Up
Quiz n Finish a Two charges Q1 = 8.6µC and Q2 5.1µC are placed on the two corners of a rectangle with the 14.8mm as shown in the figure below. How much work is required to bring 7.5mm away from Q, ? sides a = 7.2mm and b %3D HUR a thir charge Q3 = 7.5µC from infinity to point P that is a distance c= Please take k 9.0 x 10°N. m2/C? and express your answer using one decimal place in units of J or N.m. Q1 »P C a Q2 b.
Plz solve
Answer #1 only.
Prob.2. Three charges (Q1 = Q3 = 20.0nC, and Q2 = - 10.0nC) are arranged on the three %3D vertices of a triangle as shown. [a]Determine the electric potential energy (in units of UJ) of the three-charge configuration. (Example: If your answer is 4.5x10-6J = 4.5µJ, enter your answer as 4.5) 4.0cm 3.0cm- 3.0cm
All go together.
Please leave as many explanations as you can. Thank you!
Problem #1 A hollow metal sphere of radius 4 cm has a charge of 20 nC distributed evenly on the entirety of the surface. Find the surface charge density (o).
A uniform electric field with a magnitude of 1200 N/C points in the negative x direction as shown in the figure below. (a) What is the difference in the electric potential between points A and B? (b) What is the difference in the electric potential between points B and C? (c) What is the electric potential difference between points C and A? (d) Is it possible to determine the electric potential at point A or not? Explain your answer. E [1] 3.0 cm A B 4.0 cm 5.0 cm C y "L. X
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- X