# Magnetic force storage or amplification question

all forms of energy can be stored or amplified for example : capacitor , hydraulics ,laser , pulley , etc..

what is the equivalent to that for magnetic force ? can magnets be connected in series or parallel ?

A capacitor, as you pointed out, its a device capable of storing electrostatic energy. The energy is stored in the electric field formed by the capacitor, usually between the plates. As you said, you can put capacitors in series, and in parallel, forming an equivalent circuit with an equivalent overall capacitance. The stored electrostatic energy can be calculated, and the voltage of the capacitor can be calculated as well: $$U = \frac{1}{2}\frac{Q^2}{C}, \quad\quad V = \frac{Q}{C}$$

The magnetic equivalent of this, is an inductor. Its a device capable of storing magnetic energy. Same way as the capacitor, the energy is stored in the magnetic field formed by the inductor. The inductor has inductance $L$. You can put inductors in series and parallel, and the equivalent circuit will have an equivalent inductance. The magnetic energy stored can be calculated, so as its voltage: $$U = \frac{1}{2}LI^2, \quad\quad V = -L\frac{dI}{dt}$$

• For some reason I went to mechanical energy. $U$ here is energy. Are these practical ways to store energy though? Is an inductance of $2$ (units) something that can be made? (to store 2 joules at 1 amp) Commented Aug 18, 2015 at 19:25
• @AlecTeal Indeed, $U$ here is energy. The unit of inductance in SI is the Henry (H). Yes, one can make an inductor of inductance $2H$ (and it will store 1 joule at 1 amp, according to the formula). About energy storage, the resistance of the device quickly dissipate the current, so, real storage of magnetic energy can be made in an inductive circuit with no resistance (say, superconductive coils..). Commented Aug 18, 2015 at 19:30
• (I would +1 you here but I do not want to eclipse my own answer. - I will do so at a later date) Commented Aug 18, 2015 at 19:32
• i am not a physics major , but i had the crazy idea of using magnets to create propulsion in vacuum of space. not sure its practical , but keep on researching. Commented Aug 18, 2015 at 20:43

Mechanically, we can store it as potential energy

Force at a distance $x$ from a point magnet is given by: $F=\frac{k}{x^3}$ where $k$ is some constant.

Energy is force over a distance, we will move outward, not take some other path around the plane. This allows us to assume the magnets are infinitely thin and facing each other, To simplify the equations:

So assuming you move from a distance of $a$ to a distance of $b$ from the magnet, you will have done the following amount of work:

$$W=\int_a^b\frac{k}{x^3}dx=k\left[-\frac{1}{2}x^{-2}\right]_a^b$$ Which $=\frac{k}{2}(a^{-2}-b^{-2})$

Note that if $b>a>0$ then $b^2>a^2$ and so $\frac{1}{b^2} < \frac{1}{a^2}$ So $0<\frac{1}{a^2}-\frac{1}{b^2}$ - which is positive. This means $k<0$ to make the result negative. As we must do work to move the object further away from the magnet (and $b$ is where we end up, which is beyond $a$)

Any questions (this is my first actual answer here, so feedback would be great!)