5. magnet questions

# 5. magnet questions - m agnet.htm Page 1 The Magnetic Force...

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magnet.htm Page 1 Mon, Mar 3, 2003 12:41 PM The Magnetic Force According to Coulomb's Law, the electric force exerted on a static charge q by another static charge q' has the form where q and q' are the charges and r is the distance between them and r-hat is a unit vector pointing from q' to q This equation correctly gives the force on static charges but when the charges are in motion there is an extra force acting on these charges which is called the magnetic force. This force depends not only on the distance between the charges but on their velocities. If q and q ' have velocities v and v' then the magnetic force on q by q' is given by This force is a fundamental law of physics, as valid as Coulomb's Law or Newton's Law of Gravitation. Like those, it varies as 1/r 2 but unlike them there is this cross product of vectors, which is rather complicated, especially when I draw it (see next page) The direction for the force must be worked out by the right hand rule for cross products: first we cross r-hat by v' and then cross that product with v - now it will turn out that the magnetic force on q (due to q') will always be perpendicular to v. Also note that BOTH charges must be moving if the cross product is not to be zero (bottom figure next page) In the SI- system the constant has the numerical value of 1 x 10 -7 Ns 2 /C 2 although for historical reasons it is usually written as μ o /4 π so our law becomes

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magnet.htm Page 2 Mon, Mar 3, 2003 12:41 PM where μ o = 4 x 10 -7 It is interesting to compare the sizes of the electric and magnetic forces
magnet.htm Page 3 Mon, Mar 3, 2003 12:41 PM Suppose we take the two charges as moving in parallel straight lines with velocites v and v' - so the force is attractive q is pulled towards q'

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5. magnet questions - m agnet.htm Page 1 The Magnetic Force...

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