Question

Write down Divergence law in integral form:

o Derive the differential form of Divergence law from the integral form by using a integral form

Answer #1

1)Write down the coordinate free definition of divergence of a
vector field.
2)Derive an expression for the divergence of a vector field
using part 1) and using integral form of Gauss' law for the
electric field E.

(c) Write Ampere’s law in integral form. Using this form find
the volume current density J as a function of distance r from the
axis of a radially symmetrical parallel stream of electrons in a
wire if the magnetic field inside the stream varies as B(r) = µ0r 2
.Find the total current flowing in the wire with the radius r =
R.

Star from the general mole balance derive the differential form
of PFR design equation

Derive the Green’s first identity from the divergence
theorem.

Write the The Ampere—Maxwell Law. mathematical expressions
(integral form only). Explain each symbol, each detail in each of
these equations – by words. Draw sketches when they are necessary
for your explanation.

How to derive ohms law in the form V=IR from the form
J=(n(e^2)ET)/m?

Use Ohm’s Law, Kirchoff’s Voltage Law, and capacitor equations
to derive the differential equation whose solution is the voltage
response of a RC circuit.

1)The differential form of the ampere law for static conditions
is:
a)∇xB=o
b)∇xE=0
c)∇xD=pv
d)∇xH=...
2) ∇xB=0 implies for the magnetic field that:
a) is Solenoid
b)is conservative
c) Magnetic load exists
d)all of the above

Derivevthe intergral and differential form for Amperes Law from
Maxwell Equations. Thumbs up for all steps and neatly
written.

Consider the differential equation: y'' = y' + y
a) derive the characteristic polynomial for the differential
equation
b) write the general form of the solution to the differential
equation
c) using the general solution, solve the initial value problem:
y(0) = 0, y'(0) = 1
d) Using only the information provided in the description of the
initial value problem, make an educated guess as to what the value
of y''(0) is and explain how you made your guess

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