Calculate the potential energy of the interaction between two linear quadrupoles when they are collinear and their centres are separated by a distance r.
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Calculate the potential energy of the interaction between two linear quadrupoles when they are collinear and their centres are separated by a distance r.
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- An uncharged, infinitely long conducting cylinder of radius a is placed in an initially uniform clectric ficld E = Eoi, such that the cylinder's axis lics along the z axis. The resulting clectrostatic potential is V (x, y, z) = Vo for points inside the cylinder, and Ega?x x² + y? V (r, y, z) = Vo – Egx + for points outside the cylinder, where Vo is the (constant) clectrostatic potential on the conductor. Usc this expression to determine the resulting clectric ficld, E.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 Q 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 T in 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 л, α etc. use pi, alpha. For example to get 14√AB use 1/pi*A^2/B*sqrt(AB). Please use the exact variables given in the conditions of the problem: e.g if L is given, then do not use 1. For subscripts such as Fc simply write "FC" (without the quotes). Please use…A point charge 100 PC is located at (4, l , —3) while the x-axis carries charge 2 nC/m. If the plane z 3 also carries charge 5 nC/m2 , find E at (l, l, l).
- A small rod of length 1.0 cm is placed along the x-axis and has a linear charge density given by λ=αx, where α=3.0 C/cm^2 and x is measured from the center of the rod.A dipole of moment p1 lies at the origin and a dipole of p2 lies at a point whose position vector is r. Determine the force between the two dipoles. For which orientation of the dipoles does the force maximize?A small object with dipole moment p is released near its equilibriumorientation in a uniform electric field of magnitude E.The rotational inertia of the dipole is I. (a) What is the effectivetorsional constant k of this simple harmonic system? (b)Calculate the angular frequency v of small oscillations aboutthe equilibrium orientation.