Simple Nature - Light and Matter

We have found one specific example of the general law of natureknown as Ampère’s law:Γ = 4πkc 2I throughd / Positive and negative signs inAmpère’s law.Positive and negative signsFigures d/1 and d/2 show what happens to the circulation whenwe reverse the direction of the current I through . Reversing the currentcauses the magnetic field to reverse itself as well. The dotproducts occurring in the circulation are all negative in d/2, so thetotal circulation is now negative. To preserve Ampère’s law, we needto define the current in d/2 as a negative number. In general, determinethese plus and minus signs using the right-hand rule shown inthe figure. As the fingers of your hand sweep around in the directionof the s vectors, your thumb defines the direction of current which ispositive. Choosing the direction of the thumb is like choosing whichway to insert an ammeter in a circuit: on a digital meter, reversingthe connections gives readings which are opposite in sign.A solenoid example 13⊲ What is the field inside a long, straight solenoid of length l andradius a, and having N loops of wire evenly wound along it, whichcarry a current I?⊲ This is an interesting example, because it allows us to get avery good approximation to the field, but without some experimentalinput it wouldn’t be obvious what approximation to use.Figure e/1 shows what we’d observe by measuring the field of areal solenoid. The field is nearly constant inside the tube, as longas we stay far away from the mouths. The field outside is muchweaker. For the sake of an approximate calculation, we can idealizethis field as shown in figure e/2. Of the edges of the Ampèriansurface shown in e/3, only AB contributes to the flux — there iszero field along CD, and the field is perpendicular to edges BCand DA. Ampère’s law givese / Example 13: a cutawayview of a solenoid.Γ = 4πkc 2(B)(length of AB) = 4πkc 2B = 4πkηc 2= 4πkNIc 2 lI through(η)(length of AB)self-check DWhat direction is the current in figure e? ⊲ Answer, p. 927674 Chapter 11 Electromagnetism