A 9 kg particle is in a potential given by U(x) = 2 x^4 - 6 x^2 - -2 x + 8 (J). Calculate the acceleration of the particle when it is at x = 1 m, in m/s2.

(0,0,0) and the 5. The point o is the origin of the coordinate system, o = coordinates of b are b = (x,y, z). The electric potential at o is zero, V, = 0. Hence, the electric potential at b is V = – E · dr. You can take any path from o to b. (a) Here is one particular path from o to b. First move on a straight line from o to a = : (x,0,0), then from a to a' = (x, Y, 0), and finally from a' to b = (x, y, z). Make a plot of this path, indicating the coordinate system and the locations of a, a' and b. – SE • dr depends only on the y However, the line integral V coordinate of b = (x, y, z). Hence, in the following, we will focus on b = (0, y, 0) and take the straight path from o to b. (b) Compute E · dr for y d result, use this potential next.

Consider a ring of charge in the x-y plane of radius 2.7 m, centered at the origin.  The charge per angle around the ring is given by dQ/dα = a (1 - cos α)  (nC/rad), where a = 8.4 nC/rad.  Calculate the electric potential along the z axis at z = 5.8 m, in V.  Use k = 9 x 109 N m2 / C2. (Please answer to the fourth decimal place - i.e 14.3225)

A long coaxial cable carries a positive uniform volume charge density, ρ, on theinner cylinder (radius a), and a negative uniform surface charge density, σ, of thecylindrical shell (radius b). The surface charge has a magnitude so that the cable asa whole is electrically neutral.                                                                                                                                                                                                    find the electric potential V atthe center of the coaxial cable, using s = infinity as a reference point