Answer: Earth's magnetic field has flipped its polarity many times over the ... Earth has settled in the last 20 million years into a pattern of a pole reversal about ... And while reversals have happened more frequently in "recent" years, when ... per year, as opposed to about 10 miles per year in the early 20th century.
Explanation:
Answer:
a) V(r) = k*λ*r^2/R^2 r =< R
V(r) = -2*k*λ*Ln|r/R|
Explanation:
Given:
- The derived results for Electric Fields are:
r =< R, E(r) = 2*k*λ*r / R^2
r > R, E(r) = 2*k*λ/ r
Find:
-Expressions for the electric potential V as a function of r, both inside and outside the cylinder.
Solution:
- From definition we can establish the relation between E(r) and V(r) as follows:
E(r) = - dV / dr
- We will develop expression for each case as follows:
Case 1: r =< R
E(r) = 2*k*λ*r / R^2 = - dV / dr
Separate variables:
2*k*λ*r . dr / R^2 = -dV
Integrating both sides:
2*k*λ/R^2 integral(r).dr = -integral(dv)
k*λ*r^2/R^2 | = - ( 0 - V)
Put limits ( 0-r)
V(r) = k*λ*r^2/R^2
Case 2: r >= R
E(r) = 2*k*λ/ r = - dV / dr
Separate variables:
2*k*λ.dr/ r = -dV
Integrating both sides:
2*k*λ integral(1/r).dr = -integral(dv)
2*k*λ*Ln|r/R| = - ( V - 0)
Put limits ( R -> r)
V(r) = -2*k*λ*Ln|r/R|
For Art class, Social Studies class, English class, American History class,
or Photography class, Shani has done an incredible amount of work.
She'll tell her parents all about it at dinner, and her arms will really ache
when she gets up tomorrow morning.
But it's a different story in Physics class. In Physics, there is a formal definition
for "work". (That's so it can be measured, and numerically compared to all forms
of energy.)
The scientific definition of work is
(force exerted) times (distance moved) .
With this definition, if the force doesn't move through a distance,
then the work done is zero.
Anything you do without moving, even if it's holding a small car over
your head for an hour while your muscles tremble and sweat pours
down, represents no "work" in the scientific sense.
