An electron is constrained to the central axis of a ring of charge 1 coulomb and of radius 1 meter. The electrostatic force exerted on the electron can cause the electron to oscillate through the center of the ring. Find the frequency in Hertz of small-amplitude oscillation of the electron through the center of the ring. The square surface shown in the figure measures 3.4 mm on each side. It is immersed in a uniform electric field with magnitude E = 1700 N/C and with field lines at an angle of 35 with a normal to the surface, as shown. Take that normal to be "outward," as though the surface were one face of a box. Calculate the electric flux through the surface. Normal 4 Number i Units VGaussian surface An electric field given by E = ai - b(y? + c)j pierces the Gaussian cube of the figure above, where the cube has side length d. NOTE: Express your answers in terms of the variables given. (a) What is the electric flux through the top face? Ptop = (b) What is the electric flux through the bottom face? Pbottom = (c) What is the electric flux through the left face? Pleft = (d) What is the electric flux through the back face? Pback = (e) What is the net elctric flux through the cube? Inet =The cube in the figure has edge length 1.18 m and is oriented as shown in a region of uniform electric field. Find the electric flux through the right face if the electric field (a) is in the positive x direction and has magnitude 8.43 N/C, (b) is in the negative y direction and has magnitude 2.68 N/C, and (c) is in the xz plane, has x component -3.52 N/C, and has z component 4.24 N/C. (d) What is the total flux through the cube's surface for each field? (a) Number Units (b) Number Units (c) Number Units (d) Number Units