Concept explainers
Which of the following expressions are correct forms of Gauss’s law?
a.
b.
c.
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Physics for Scientists and Engineers: Foundations and Connections
- In Thomson’s model, an atom is a positively charged spherical material in which negatively charged electrons are embedded like chocolate chips on a ball of cookie dough. Consider such an atom, made up of a uniformly charged sphere with charge +e and radius R and a point charge with mass m and charge −e. a. Locate the position of electrostatic equilibrium for the electron inside the sphere. b. Assume further that the sphere has little or no resistance to the electron’s mo- tion. If the electron is displaced from equilibrium by a distance less than R, show that the resulting motion of the electron would be simple harmonic. c. If the electron was displaced from equilibrium by a distance greater than R, would the electron oscillate? Would its motion be simple harmonic?arrow_forwardThe HCl molecule has a dipole moment of about 3.4x10-30 C·m. The two atoms areseparated by about 1.0x10-10 m.a. What is the net charge on each atom? Is this equal to an integer multiple of e? Ifnot, explain.b. What maximum torque would this dipole experience in a 2.5x104 N/C electricfield?c. How much energy would be needed to rotate one molecule 45° from itsequilibrium (lowest potential energy) position?arrow_forwardUsing 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_forward
- A carbon atom's nucleus and its electrons become separated by 20nm. What is the magnitude of the force the nucleus feels towards the electrons in N?arrow_forwardWhat would be the total force (in nN) between two ions of substance1 when the distance between them is 0.236 nm? The attraction and repulsion energy coefficients between their ions are shown below (the respective energies are in ev units) A B Substance1 1.436 7.32E-06 8. Select one O a 21 Ob 1.42 OcCO O d -62 O e 9.5arrow_forward(a) What is the magnitude of the angular momentum for an l=1 electron? (b) Calculate the magnitude of the electron's spin angular momentum. (c) What is the ratio of these angular momenta?arrow_forward
- electrons Two protons (p) and two (e) are arranged on a circle of 5 [cm], with angles 0₁ = 20°, 0₂ = 60°, 03 = 20° and 04 = 60°, as radius r shown in the figure. (qp = +1.6 x 10-1⁹ [C] and qe = -1.6 × 10-19 [C]). The figure is not to scale. 04 y a. Find Enet, the net electric field vector produced at the center of the circle. Enet =([ ])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 Ēnet (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). Р Xarrow_forwardA uranium ion and an iron ion are separated by a distance of ?=57.10 nm, as shown in the figure. 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 ?U of the force on the electron from the uranium ion?arrow_forward2. A vector field is specified as G = (24xy) ax + 12(x^2 + 2)ay + (18 z^2)az. Given two points, P(1, 2,-1) and Q(-2, 1, 3), find: a) G at P b) a unit vector in the direction of G at Q c) a unit vector directed from Q toward Parrow_forward
- 9. The permanent electric dipole moment of the water molecule (H₂O) is 6.2 × 10-30 C.m. What is the maximum possible torque of a water molecule in a do- mestic microwave oven with 121.3 V/m electric field? 8 H 104.5⁰ 8+arrow_forwardAn electron and a mystery charge 5.3 × 10^−11 m apart attract each other with a force of 2.61 × 10^12 N. Calculate the value of the mystery charge (in C). The answer (in fundamental SI unit) is ___________ (type the numeric value only)arrow_forwardAn electron and a mystery charge 5.3 × 10^−11 m apart attracts each other with a force of 2.61 × 10^12 N. Calculate the value of the mystery charge (in C). The answer (in fundamental SI unit) is ___________arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College