Consider a uniformly charged sphere of radius rand total charge q. the electric field eout outsidethe sphere (r≥r) is simply that of a point charge q. the electric field ein inside the sphere (r≤r) is radially outward with field strengthein=1/4πϵ0(q/r^3)rthe electric potential vout outside the sphere is that of a point charge q. find an expression for the electric potential vin at position r inside the sphere. as a reference, let vin=vout at the surface of the sphere. what is the ratio vcenter/vsurface? graph v versus r for 0≤r≤3r.

Two horizontal plates with infinite length and width are separated by a distance h in the z direction. the bottom plate is moving at a velocity u. the incompressible fluid trapped between the plates is moving in the positive x-direction with the bottom plate. align gravity with positive z. assume that the flow is fully-developed and laminar. if the systems operates at steady state and the pressure gradient in x-direction can be ignored, do the following: 1. sketch your system 2. identify the coordinate system to be used. 3. show your coordinates and origin point on the sketch. list all your assumptions. 5. apply the continuity equation to your system. nts of navier stokes equations of choice to your system 7. solve the resulting differential equation to obtain the velocity profile within the system make sure to list your boundary conditions. check units of velocity 8. describe the velocity profile you obtain using engineering terminology. sketch that on the same sketch you provided in (1). 9. obtain the equation that describes the volumetric flow rate in the system. check the units.

Which type of wave can travel without a medium

Física: un futbolista patea hacia el arco con una velocidad de 15m/ah, calcular: a)el alcance para un ángulo de tiro de 25? , b) el tiempo que el balón permanece en el aire.