# Energy Formulas with the form (1/2)ab^2

1. May 13, 2012

### krismath

1. The problem statement, all variables and given/known data
Can anybody help me think of Energy formulas/equations in the form below?
Any form of Energy.
(Please also state what does each variable stands for.)

2. Relevant equations

$E = \frac{1}{2}ab2 = \frac{1}{2}ac$

Where c = ab

3. The attempt at a solution

So far, this is what I came up with:
Kinetic Energy: $E = \frac{1}{2}mv2 = \frac{1}{2}pv$
M = Mass
V = Velocity
P = Momentum = M x V

Capacitor: $E = \frac{1}{2}CV2 = \frac{1}{2}QV$
C = Capacitance = Q/V
V = Voltage
Q = Charge

Spring : $E = \frac{1}{2}kx2 = \frac{1}{2}Fx$
K = Spring Constant
X = Extension of Spring
F = Force Acted = K x X

Self-inductance : $E = \frac{1}{2}LI2 = \frac{1}{2}∅_{B} I$
L = Self-Inductance
I = Current
B = Magnetic Flux = L x I

2. May 14, 2012

### BruceW

Those all look like good examples to me. How many do you need to find?

3. May 14, 2012

### krismath

It says: "As many as you can"

4. May 14, 2012

### DeIdeal

How about the energy densities of electric and magnetic fields. They fit the "½ab²" requirement, but are not strictly speaking formulas of energy.

5. May 14, 2012

### krismath

OK, I will try to look up that one (and post it in here, for reference to other people in the future that might need it.)

6. May 14, 2012

### flatmaster

The energy density term in Bernoulli's equation would also fit into this category.

7. May 14, 2012

### krismath

Okay, now I found it,

Electric Field Energy Density: $Energy (per volume) = \frac{1}{2}\ \epsilon_{o}\ E^{2}$
$\epsilon_{o}\ =\ 8.854187817\ \times\ 10^{-12}\ F\ m^{-1}$ = Electric Constant
E = Electric Field

Magnetic Field Energy Density: $Energy (per volume) = \frac{1}{2}\ \frac{1}{ \mu_{o}\ }\ B^{2}$

$\mu_{o}\ =\ 4\pi\ \times\ 10^{-7}$ = Magnetic Constant
B = Magnetic Field

Last edited: May 14, 2012
8. May 14, 2012

### krismath

Hmmm... But on what I have learned in my class, that term is derived from the Kinetic Energy, isn't it?

9. May 14, 2012

### DeIdeal

Yeah, those were the ones I was talking about. And if you want to write them like this:

$E = \frac{1}{2}ab^{2} = \frac{1}{2}bc,\quad c=ab$

You can do so:

$u_{E} = \frac{1}{2}\epsilon_{0} E^{2} = \frac{1}{2} \vec E \cdot \vec D ,\quad D =\epsilon_{0} E$

$u_{B} = \frac{1}{2}\frac{1}{\mu_{0}} B^{2} = \frac{1}{2} \vec B \cdot \vec H ,\quad H =\frac{B}{\mu_{0}}$

Where D and H are the electric displacement field and the strength of a magnetic field, respectively, if you haven't seen them before.

10. May 14, 2012

### krismath

Thank you very much!