Aparallel plate capacitor of plate area a and plate separation b is filled with a dielectric substance whose dielectric constant is k = 1 + x/b where the x-axis is perpendicular to the plates and the plates are at x = 0 and x= b. neglecting fringing effects, find the capacitance of the capacitor the electric field, electric displacement, and polarization when a potential difference vis applied between the plates. the free surface charge density on the plates, the bound volume charge inside the dielectric, and the bound surface charge on the surface of the dielectric when a potential difference vis applied between the plates.

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 740 n/m. it is initially at rest on an inclined plane that is at an angle of theta= 26 with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is uk = 0.17. in the initial position, where the spring is compressed by a distance of d = 0.16 m, the mass is at its lowest position and the spring is compressed the maximum amount. take the initial gravitational energy of the block as zero. the block's initial mechanical energy is 9.472 j.b. if the spring pushes the block up the incline, what distance l in meters will the block travel before coming to rest? the spring remains attached to both the block and the fixed wall throughout its motion.