Two very large thin spherical shells of radii a = 16.8m and b= 23.1m carry uniform charges Q and -Q as shown in the figure below. If the electric field between the shells is E =k where Q = 3.29µC. Determine the potential difference between the shells, V (b)– V(a). Express your answer in units of Volts using one decimal place. Take the value of the Coulomb's constant as k= 9z10 N. m/C. %3D -Q
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- A uniform ring of charge, in the xy plane, centered on the origin, has radius R, and total charge Q. What is the voltage on the z-axis at position z=h? Give the answer in terms of R, Q, h and the constant \epsilon . As usual assume that the voltage at infinity is zero. V(h)=Consider a system consisting of two protons that are separated by a distance of 25 nm. Now, replace one proton with an electron, and position the two charges at a distance of 5 nm apart from each other. Compare the new Coulombic force with the one in the first scenario: a.It switches from repulsive to attractive and is 5x the original value b. It switches from attractive to repulsive and is 1/5th the value of the original c. It switches from repulsive to attractive and is 25x the value of the original d. It switches from repulsive to attractive and is 1/25th the value of the original e. There is no change in the Coulombic force because the charges are equalSuppose 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 ry has charge -Q. The electric field E at a radial distance r from the central axis is given by the function: E = aer/a0 + B/r + bo where alpha (a), beta (8), an 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: Vah = Edr= - Fdr Calculating the antiderivative or indefinite integral, Vab = (-aager/a0 +8 + 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"b/a0 .eralao) + B In( )+ bo ( ))
- = 1.602 × 19 = Problem 19.02. A molecule with mass m = 9.11 × 10-25 kg and net charge de 10-1⁹ C is accelerated from rest across a potential difference of V = 200 V. (a) What is the molecule's change in potential energy ¡U? (b) What is the molecule's final velocity vf?Calculate the magnitude of the Coulomb force between 2 hydrogen ions, H each with a charge of +e on them, at a distance of (9.6x10^0) nm . Use 2 sf in your calculation. Note: Your answer is assumed to be reduced to the highest power possible. Your Answer: x10 AnswerTwo 0.01 m radius spherical +1.0 µC uniform charge distributions are placed 0.2 m apart. How much electrical energy is contained in this system? It requires energy to form each of the spherical charge distributions as well as bring the two spheres together. Let us call the energy required to form the spherical charge distribution Wformation: Let us call the energy required to assemble or bring together the charges Wassembly: So, Wtotal = 2 x Wfor Formation + Wassembly The energy Wformation (in Joules) can be calculated as follows: 3 Q? Wformation 5 4πεα Where Q is the total charge of the sphere in Coulombs and a is the radius of the sphere in
- In the Millikan oil drop experiment, the charge of an electron is measured by placing an ionized oil drop of mass, m, and net charge, e, between the conducting plates of a parallel plate capacitor that produces a vertically downward electric field as shown in the diagram below. If the electron is in static equilibrium between the plates, which of the following is the correct expression for the electron charge of magnitude e? The voltage difference between the capacitor plates is V and the distance between the plates is d. a. V/(mgd) b. mgV/d c. d/(mgV) d. Vd/mg e. mgd/VFour equal positive charges, of magnitude 10-6 C are situated at the corners of a square, with a length of side equal to 0.25m. A small test charge of 10-9 C is placed at location X, in the exact center of the square. What is the magnitude of the potential energy of the test charge and what is the voltage at X? If the test charge is released what is its final velocity, taking its mass to be 1.5g?For each of the following situations, determine if there is an induced current in the loop, and if so, find the direction of the induced current. Defend your answers.
- Two point charges of mass m each are suspended in the gravitational field of the Earth by two non-conducting massless strings, each of length 1, attached to the same fixed point. The spheres are given equal charges of the same sign. As a result each string makes angle a to the vertical (see figure below). Write down an expression for the tension of a string Tin terms of Coulomb force Fc between the charges and the angle a. Use the following notation (without the quotes): "/" for division, "*" for multiplication, "+" an "-" as usual. For powers used "^2", while for square root use "sqrt". To indicate that square root applies to the whole expression use brackets - for example, for √AB use sqrt(A*B). For Greek letters such as , a etc. use pi, alpha. For example to get √AB use 1/pi*A^2/B*sqrt(AB). Please use the exact variables given in the conditions of the problem: e.g 1 if L is given, then do not use 1. For subscripts such as Fe simply write "FC" (without the quotes). Please use…Two uncharged spheres are separated by 3.00 m. If 1.30 x 1012 electrons are removed from one sphere and placed on the other, determine the magnitude of the Coulomb force (in N) on one of the spheres, treating the spheres as point charges. HINT NV is the energy (in J) required to bring the two charges from infinite distance separation to distance r (in nm).Q1 and Q2 are the charges in terms of electrons.(i.e. the constant in the above expression is 2.31×10-19 J nm electrons-2) For a group of "point" charges (e.g. ions) the total energy of interaction is the sum of the interaction energies for the individual pairs. Calculate the energy of interaction for the square arrangement of ions shown in the diagram below.