Simple Nature - Light and Matter

d/Positive and negative signs in Ampere’s law.` e/Example 13: a cutaway view of a solenoid. the products of the vectors’ magnitu ...

f/A proof of Ampere’s law.` and DA. Ampere’s law gives` Γ= 4 πk c^2 It hr ough (B)(length of AB) = 4 πk c^2 (η)(length of AB) B= ...

square dipole. This part of the proof can be most easily accom- plished by the methods of section 11.4. It should, for example, ...

g/Discussion question A. h/Discussion question B. i/Discussion question C. j/Discussion question D. k/Discussion question E. hav ...

a/The div-meter, 1, and the curl-meter, 2 and 3. 11.4 Ampere’s law in differential form (optional)` 11.4.1 The curl operator The ...

b/The coordinate system used in the following examples. c/The fieldxˆ. d/The fieldˆy. e/The fieldxˆy. Note that the curl, just l ...

f/The field−yxˆ. g/Example 14. h/Example 15. by evaluating the field at the midpoints of its sides, x=s/ 2 y= 0 F= (s/2)yˆ s 1 · ...

is very much as it was before, except that all the field vectors have had one unit worth ofyˆadded to them. But what do we get i ...

i/A cyclic permutation of x, y, andz. j/Example 17. i.e., F=axxˆ+byˆx+cxˆ+dxyˆ+eyyˆ+fˆy. The only terms whose curls we haven’t y ...

so curlE= cosˆz This is visually reasonable: the curl-meter would spin if we put its wheel in the plane of the page, with its ax ...

k/A summary of the derivative, gradient, curl, and divergence. 11.5 Induced electric fields 11.5.1 Faraday’s experiment Nature i ...

a/Faraday on a British ban- knote. b/Faraday’s experiment, sim- plified and shown with modern equipment. ture of 19th century En ...

c/Detail from Ascending and Descending, M.C. Escher, 1960. d/The relationship between the change in the magnetic field, and the ...

f/A generator. g/A transformer. The generator example 18 A basic generator, f, consists of a permanent magnet that rotates withi ...

h/It doesn’t matter whether it’s the coil or the permanent magnet that spins. Either way, we get a functioning generator. the ma ...

i/A generator that works with linear motion. figure h/1, which implies the existence of induction effects. But this example invo ...

j/A new version of figure i with a tiny loop. The point of view is above the plane of the loop. In the frame of reference where ...

perpendicular to the front and back sides of the loop, BC and DA, so there is no contribution to the circulation along these sid ...

k/Example 21. A changing magnetic flux makes a curly electric field. You might think based on Gauss’ law for magnetic fields tha ...

l/Example 22. variation of the magnetic field is on the order of (10^9 T/ 104 m) = 105 T/m. If you can run north at the same spe ...