A parallel plate capacitor with a nonuniform dielectric

A parallel plate capacitor with a nonuniform dielectric The dielectric of a parallel plate capacitor has a permittivity that varies as ero+ax, where x is the distance from one plate. The area of a plate is A, and their spacing is s. (a) Find the capacitance. (b) Show that, if er varies from ero to 2ero, then c is 1.44 times as large as if a were zero. (c) Find P from the values of D and E for that case. (d) Deduce the value of rb. (e) Now calculate rb from the relation given in problem 7-2 [Prob 7-2: show that in a non homogeneous dielectric, if rf = 0, then rb = (ero/er) E.grad er] (f) Draw curves of e, rb and P as functions of x for ero = 3.00, a = ero/s, s = 1.00 mm when the... click for more

Electrostatic potential energy of a distribution of charges.

Three point charges are on the x axis: q1 at the origin, q2 at x=3 m, and q3 at x= 6 m. Find the electrostatic potential energy for (a) q1=q2=q3=2uC (u is the fancy u sign); (b) q1=q2=2uC, and q3 -2uC; and (c) q1=q3 = 2uC, and q2= -2uC.

Grounded cylindrical infinite conductor is placed in a uniform electric field. To show that V = -Eo(1 - a^2/p^2)pcos(phi) satisfies Laplace's equation.

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Equality of two integrals and the volume integral

Please just complete the first part, no other restrictions on the density. See attached file for full problem description.

Derive the Equation of Motion

Derive the Equation of Motion. See attached file for full problem description.