Dielectric boundary conditions. At the interface between two dielectric materials with dielectric constants ε1 and ε2, the electric field intensity everywhere in material 1, � 1, has magnitude 1 and makes an angle α1 with the normal to the interface between the materials. There is a charge with surface charge density rhos sandwiched between the two materials. Determine the charge density rhos such that the electrical field intensity in material 2, �2 , is exactly equal to � 1.

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 790 n/m. it is initially at rest on an inclined plane that is at an angle of 28 degrees with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is k = 0.14. in the initial position, where the spring is compressed by a distance of a = 0.18 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. 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.

The image below shows numerous volcanic mountains in the pacific northwest. what is the most likely cause of the volcanic and earthquake activity in this region?

Imagine that someone pushes one marble toward a motionless marble. would there still be action-reaction forces involved in the collision? how might the marbles’ motions be changed? ?