Calculate the potential energy of the interaction between two linear quadrupoles when they are collinear and their centres are separated by a distance r.

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).