Okay so Jfree=J. also D=εE so E=D/ε
and therefore J=σD/ε
edit:
so
∇ · σD/ε = −∂(ρfree)/∂t
or
(∇σ/ε)· D + (σ/ε)(ρfree) = −∂(ρfree)/∂t
Doesn't feel like im getting anyhere
I could sub the first eq into the second to get the divergence of current density equals the negative differential of the divergence of the electric displacement field, or
∇ · Jfree = −∂(∇ · D)/∂t
Can Jfree and total J be considered to be the same thing in this example? Also I will lose ρ...
Homework Statement
Show that any charge distribution in a conductor of conductivity σ and relative
permittivity κ vanishes in time as ρ = ρ0exp(−t/ζ) where ζ = κǫ0
σ
Homework Equations
Maxwell's equation
∇ · D = ρfree
equation of continuity for a free charge density
∇ · Jfree =...
ive just tried substituting the particular integral
y(x)= c1(x^2)sin(x)+c2(x^2)cos(x)+xc3sin(x)+xc4cos(x) into y"+y=xsinx. I end up with
2c1sin(x)+4xc1cos(x)+2c2cos(x)-4xc2sin(x)+2c3cos(x)-2c4sin(x)=xsin(x)
This doesn't look solvable. Ive checked my differentiating a couple of times and...
thanks. thats really helpful. is there anyway of knowing what the particular integral is for any unhomogenous second order differential equation, or is it just trial and error?
Homework Statement
solve y"+y=xsin(x) , initial conditions y(0)=0, y'(0)=1
Homework Equations
The Attempt at a Solution
I know that when right hand side equals something like sin(x), then the particular integral is xc1sin(x)+xc2cos(x). I am unsure what the particular integral...
I understand that people are only helping voluntarily. It is just a bit frustrating watching new topics popping up at the top which get replies very quickly and then watching my topic move further and further down the page.
[SOLVED] Satisfying wave equation
Homework Statement
Confirm that the following wave satisfies the wave equation and obtain an expression for the velocity of a wave
Y=Asin(2x-5t)*e^(-2t)
Homework Equations
the wave equation is
(d^2y/dt^2)=(V^2)*(d^2y/dx^2)
The Attempt at a...
Homework Statement
I need to calculate the zero point of the telescope and camera i used.
Homework Equations
The Attempt at a Solution
I have count rates of various points on the screen in a 19x19 pixel box of a standard star using the two filters V and R. Ive used exposure...
1. Homework Statement
A wedge with mass M rests on a frictionless horizontal table top. A block with mass "m" is placed on the wedge. There is no friction between the block and the wedge. The system is released from rest.
A. Calculate the acceleration of the wedge.
B. Calculate the...