For r<a the electric field must be 0. At r=a there is a surface charge over the sphere giving an E(r=a)=q/4*pi*ε_0*a^2. a<r<R E will change by dividing by ε(r).
The continuity equation states that the change in bound charge density with respect to time will equal the negative value of the divergence of bound current density.
For this problem it is a static case so it makes sense, change in charge density is 0 and there is no current density.
The bound...
So with that being said, the D field outside (region 3) essentially becomes the what the electric field would be in that region (multiplied by ε_0 of course). D (r>R) = q/(4*pi*r^2), units of C/m^2 look good.
I know that inside region 1, the D-field is zero as it is a conducting sphere, the E-field must be zero. It makes sense that in region 2 (inside the dielectric) there is a D-field.
My question is, is there a D-field outside the dielectric material (r>R)? Obviously there will be an E-field, but...
would separating the equation such that D = (∂u/∂t)((∂x^2)/(d^2u)) be of any help? Would the spatial dimensions cancel eacher out just giving dx^2/dt so units of m^2/s?
Let u be density of something (heat, smell, etc.). Assume the something only diffuses; there’s no convection or ballistic transport. Let’s work in one spatial dimension (x). Then u satisfies the diffusion equation,
∂u/∂t = D ((∂^2)u/(dx^2))
What is the dimensionality, N, of the Hilbert space (i.e., how many basis vectors does it need)?
To be honest I am entirely lost on this question. I've heard of Hilbert space being both finite and infinite so I'm not sure as to a solid answer for this question. Does the Hilbert space need 4...
Since the box is parallel to the stairs though I thought I could assume the box was horizontal. How would I implement the 45 degrees into my calculation of the moment?
Two friends are carrying a 200kg crate up a flight of stairs. The crate is 1.25m long and 0.500m high and its center of gravity is at its center. The stairs make a 45 degree angle with respect to the floor. The crate is also at a 45 degree angle so the bottom side of crate is parallel to the...