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05 September 2003

Gravity and Electricity

by George Hrabovsky, President of MAST

News from MAST

Di is working on some cool stuff in number theory, no word on when she will have something for publication; but it should be within a few weeks.

Two Fields and Two Forces

Last time we briefly discussed the basic idea of fields.  This time we will discuss the forces associated with each of the fields.  We have discussed gravitational fields once before; but that was a long time ago, (several columns beginning with, "Gravity.")  Recall that the force exerted on an object of mass m_1 by another object with mass m_2 separated by some distance ris given by,

F = (G m_1 m_2)/r^2 .

Where FormBox[RowBox[{G, , ≈, , StyleBox[RowBox[{6.67, , x, , 10^(-11), , m^3 · kg^(-1) · s^(-2)}], FontSize -> 18]}], TraditionalForm] and is called the gravitational constant.  This formula can be put into vector form,

F = - (G m_1 m_2)/r^3Overscript[r,^] .

Note that this force is always negative, that is the masses always attract each other.

There is a similar force law for electric force that was derived directly from experimental results.  The force exerted by a quantity of charge q_1 by another charge q_2 is often called Coulomb's law,

F = (k q_1 q_2)/r^3Overscript[r,^] .

It is important to note that if the charges have the same same sign the force between them will be positive, that is it will repel the forces.  If the charges have opposite signs, then they attract each other.  In SI units, the force law looks like this,

F = 1/(4 π ϵ_0) ( q_1 q_2)/r^3Overscript[r,^] .

Here ϵ_0 is the permittivity of space introduced in , "The Beginning of Einstein's Legacy."  Next time we will examine how these forces can tell us about the gravitational and electric fields.

Theory Challenge

How do we deal with the forces due to multiple masses or charges?

Created by Mathematica  (September 4, 2003)