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B-Field Distributions and Flux Plots

B-Field Distributions and Flux Plots
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2017-01-20 04:43
VectorFunctionIntegral
This example demonstrates B-field distributions and flux plots. Core mathematical concepts include vectors, functions, and integrals. Using GeoGebra commands such as Circle, Integral, Point, etc., the B-field distribution and flux plots are constructed. Suitable for university physics and mathematics courses.

GeoGebra Commands & Parameters

  1. Circle((0, 0), 2) → c2
  2. Integral(f1, 6, 14) → u
  3. Point(f1) → B
  4. CircleArc(A, B, C) → c
  5. Point(c) → D
  6. Vector(D, E) → v
  7. Point(f1) → F
  8. Vector(F, G) → w
  9. Vector(Q, T) → a
  10. Point(f1) → H
  11. Point(f1) → I
  12. Circle((0, 0), 2.01) → c31
  13. Circle((0, 0), 1.84) → c22
  14. Function(f1, 6, 14) → f
  15. Circle((0, 0), 1.7) → c4
  16. Point(c4) → K
  17. Rotate(K, θ) → W
  18. Segment(A, J) → d
  19. Angle(J, A, W) → qq
  20. Rotate(Circle[P1, (0.4 * sin((3 * β)))], (3 * β) + θ) → s3
  21. Rotate(Circle[P1, (0.4 * sin((2 * β)))], (2 * β) + θ) → s2
  22. Rotate(Circle[P1, (0.4 * sin((4 * β)))], (4 * β) + θ) → s4
  23. Rotate(Circle[P1, (0.4 * sin((5 * β)))], (5 * β) + θ) → s5
  24. Rotate(Circle[P1, (0.4 * sin((6 * β)))], (6 * β) + θ) → s6
  25. Rotate(Circle[P1, (0.4 * sin((7 * β)))], (7 * β) + θ) → s7
  26. Rotate(Circle[P1, (0.4 * sin((8 * β)))], (8 * β) + θ) → s8
  27. Rotate(Circle[P1, (0.4 * sin((9 * β)))], (9 * β) + θ) → s9
  28. Rotate(Circle[P1, (0.4 * sin(β))], β + θ) → s1
  29. Rotate(N1, β + θ) → N2
  30. Rotate(N1, (2 * β) + θ) → N3
  31. Rotate(N1, (3 * β) + θ) → N4
  32. Rotate(N1, (4 * β) + θ) → N5
  33. Rotate(N1, (-β) + θ) → N_2
  34. Rotate(N1, θ) → N11
  35. Rotate(N1, (-2 * β) + θ) → N_3
  36. Rotate(N1, (-3 * β) + θ) → N_4
  37. Rotate(N1, (-4 * β) + θ) → N_5
  38. Rotate(Circle[P1, (0.4 * sin((10 * β)))], (10 * β) + θ) → s10
  39. Rotate(Circle[P1, 0], 0 + θ) → s0
  40. Rotate(Circle[P1, ((-0.4) * sin((11 * β)))], (11 * β) + θ) → s11
  41. Rotate(Circle[P1, ((-0.4) * sin((12 * β)))], (12 * β) + θ) → s12
  42. Rotate(Circle[P1, ((-0.4) * sin((13 * β)))], (13 * β) + θ) → s13
  43. Rotate(Circle[P1, ((-0.4) * sin((14 * β)))], (14 * β) + θ) → s14
  44. Rotate(Circle[P1, ((-0.4) * sin((15 * β)))], (15 * β) + θ) → s15
  45. Rotate(Circle[P1, ((-0.4) * sin((16 * β)))], (16 * β) + θ) → s16
  46. Rotate(Circle[P1, ((-0.4) * sin((17 * β)))], (17 * β) + θ) → s17
  47. Rotate(Circle[P1, ((-0.4) * sin((18 * β)))], (18 * β) + θ) → s18
  48. Rotate(Circle[P1, ((-0.4) * sin((19 * β)))], (19 * β) + θ) → s19
  49. Rotate(S1, β + θ) → S2
  50. Rotate(S1, (2 * β) + θ) → S3
  51. Rotate(S1, (4 * β) + θ) → S5
  52. Rotate(S1, (-β) + θ) → S_2
  53. Rotate(S1, (-2 * β) + θ) → S_3
  54. Rotate(S1, (-3 * β) + θ) → S_4
  55. Rotate(S1, (-4 * β) + θ) → S_5
  56. Rotate(S1, (3 * β) + θ) → S4
  57. Rotate(S1, θ) → S11
  58. Rotate(V1, θ) → V
  59. Vector(V) → b
  60. Circle((0, 0), 1.33) → c32
  61. Circle((0, 0), 1.3) → c3
  62. Circle((0, 0), 3.51) → c11
  63. Circle((0, 0), 3.5) → c1
  64. Point(d) → L
  65. Point(d) → M
  66. Segment(L, M) → e
  67. Sequence(Segment[Rotate[L, (-asin(1 - k / j))], Rotate[M, (-asin(1 - k / j))]], k, 1, j) → z2
  68. Sequence(Segment[Rotate[L, acos(1 - k / j) + 3.141592653589793 / 2], Rotate[M, acos(1 - k / j) + 3.141592653589793 / 2]], k, 1, j) → z3
  69. Sequence(Segment[Rotate[L, asin(1 - k / j)], Rotate[M, asin(1 - k / j)]], k, 1, j) → z1
  70. Rotate((1.0791742935578592, 0.7750466243220067), θ) → N
  71. Rotate((1.6244657241348275, 1.1666666666666665), θ) → O
  72. Element(z1, 6) → qq6
  73. Rotate((1.2177290821973479, 0.5314605423922333), θ) → P
  74. Rotate((1.833030277982336, 0.8), θ) → S
  75. Segment(Rotate[(1.2177290821973479, 0.5314605423922333), θ], Rotate[(1.833030277982336, 0.8), θ]) → q6
  76. Rotate((1.2674526134856594, 0.398595406794175), θ) → U
  77. Rotate((1.9078784028338913, 0.6000000000000001), θ) → Z
  78. Sequence(Segment[Rotate[L, (-acos(1 - k / j)) - 3.141592653589793 / 2], Rotate[M, (-acos(1 - k / j)) - 3.141592653589793 / 2]], k, 1, j) → z4
  79. Element(z1, 7) → qq7
  80. Segment(Rotate[(1.2674526134856594, 0.398595406794175), θ], Rotate[(1.9078784028338913, 0.6000000000000001), θ]) → q7
  81. Element(z1, 8) → qq8
  82. Rotate((1.3018071472837596, 0.26573027119611653), θ) → A_1
  83. Rotate((1.9595917942265424, 0.3999999999999999), θ) → B_1
  84. Segment(A_1, B_1) → q8
  85. Rotate((1.0629210847844666, 0.7971908135883498), θ) → C_1
  86. Rotate((1.6, 1.2), θ) → D_1
  87. Segment(C_1, D_1) → q4
  88. Element(z1, 3) → qq3
  89. Rotate((0.9488468565221743, 0.9300559491864081), θ) → E_1
  90. Rotate((1.4282856857085702, 1.4), θ) → F_1
  91. Segment(E_1, F_1) → q3
  92. Element(z1, 2) → qq2
  93. Rotate((0.7971908135883498, 1.0629210847844666), θ) → G_1
  94. Rotate((1.2, 1.6), θ) → I_1
  95. Segment(G_1, I_1) → q2
  96. Element(z1, 1) → qq1
  97. Rotate((0.5791456991917646, 1.1957862203825247), θ) → J_1
  98. Rotate((0.8717797887081347, 1.8), θ) → K_1
  99. Segment(J_1, K_1) → q1
  100. Element(z1, 4) → qq4
  101. Element(z1, 5) → qq5
  102. Segment(Rotate[(1.1506458270518263, 0.6643256779902915), θ], Rotate[(1.7320508075688772, 1), θ]) → q5
  103. Element(z1, 9) → qq9
  104. Rotate((1.3219914074953556, 0.13286513559805826), θ) → L_1
  105. Rotate((1.98997487421324, 0.19999999999999996), θ) → M_1
  106. Segment(L_1, M_1) → q9
  107. Rotate((0.5791456991917646, -1.1957862203825247), θ) → N_1
  108. Rotate((0.8717797887081347, -1.8), θ) → O_1
  109. Segment(N_1, O_1) → w1
  110. Rotate((0.7971908135883498, -1.0629210847844666), θ) → P_1
  111. Rotate((1.2, -1.6), θ) → Q_1
  112. Segment(P_1, Q_1) → w2
  113. Rotate((0.9488468565221743, -0.9300559491864081), θ) → R_1
  114. Rotate((1.4282856857085702, -1.4), θ) → S_1
  115. Segment(R_1, S_1) → w3
  116. Rotate((1.0629210847844666, -0.7971908135883498), θ) → T_1
  117. Rotate((1.6, -1.2), θ) → U_1
  118. Segment(T_1, U_1) → w4
  119. Rotate((1.1506458270518263, -0.6643256779902915), θ) → V_1
  120. Rotate((1.7320508075688772, -1), θ) → W_1
  121. Segment(V_1, W_1) → w5
  122. Rotate((1.2177290821973479, -0.5314605423922333), θ) → Z_1
  123. Rotate((1.833030277982336, -0.8), θ) → A_2
  124. Segment(Z_1, A_2) → w6
  125. Rotate((1.2674526134856594, -0.398595406794175), θ) → B_2
  126. Rotate((1.9078784028338913, -0.6000000000000001), θ) → C_2
  127. Segment(B_2, C_2) → w7
  128. Rotate((1.3018071472837596, -0.26573027119611653), θ) → D_2
  129. Rotate((1.9595917942265424, -0.3999999999999999), θ) → E_2
  130. Segment(D_2, E_2) → w8
  131. Rotate((1.3219914074953556, -0.13286513559805826), θ) → F_2
  132. Rotate((1.98997487421324, -0.19999999999999996), θ) → G_2
  133. Segment(F_2, G_2) → w9
  134. Rotate((-0.5791456991917645, 1.1957862203825247), θ) → H_2
  135. Rotate((-0.8717797887081344, 1.8), θ) → I_2
  136. Rotate((-0.7971908135883496, 1.0629210847844666), θ) → J_2
  137. Rotate((-1.1999999999999997, 1.6000000000000003), θ) → K_2
  138. Rotate((-0.9488468565221743, 0.9300559491864081), θ) → L_2
  139. Rotate((-1.4282856857085702, 1.4), θ) → M_2
  140. Rotate((-1.0629210847844666, 0.7971908135883498), θ) → O_2
  141. Rotate((-1.1506458270518265, 0.6643256779902914), θ) → Q_2
  142. Rotate((-1.7320508075688774, 0.9999999999999999), θ) → R_2
  143. Rotate((-1.2177290821973479, 0.5314605423922332), θ) → T_2
  144. Rotate((-1.833030277982336, 0.7999999999999999), θ) → U_2
  145. Rotate((-1.2674526134856592, 0.3985954067941752), θ) → V_2
  146. Rotate((-1.907878402833891, 0.6000000000000004), θ) → W_2
  147. Rotate((-1.3018071472837596, 0.26573027119611686), θ) → Z_2
  148. Rotate((-1.9595917942265424, 0.4000000000000004), θ) → A_3
  149. Rotate((-1.3219914074953556, 0.1328651355980584), θ) → B_3
  150. Rotate((-1.98997487421324, 0.20000000000000015), θ) → C_3
  151. Rotate((0.5791456991917646, -1.1957862203825247), θ) → D_3
  152. Rotate((0.8717797887081347, -1.8), θ) → E_3
  153. Segment(D_3, E_3) → e1
  154. Rotate((0.7971908135883498, -1.0629210847844666), θ) → F_3
  155. Rotate((1.2, -1.6), θ) → G_3
  156. Segment(F_3, G_3) → e2
  157. Rotate((0.9488468565221743, -0.9300559491864081), θ) → H_3
  158. Rotate((1.4282856857085702, -1.4), θ) → I_3
  159. Segment(H_3, I_3) → e3
  160. Rotate((1.0629210847844666, -0.7971908135883498), θ) → J_3
  161. Rotate((1.6, -1.2), θ) → K_3
  162. Segment(J_3, K_3) → e4
  163. Rotate((1.1506458270518263, -0.6643256779902915), θ) → L_3
  164. Rotate((1.7320508075688772, -1), θ) → M_3
  165. Segment(L_3, M_3) → e5
  166. Rotate((1.2177290821973479, -0.5314605423922333), θ) → O_3
  167. Rotate((1.833030277982336, -0.8), θ) → P_3
  168. Segment(O_3, P_3) → e6
  169. Rotate((1.2674526134856594, -0.398595406794175), θ) → Q_3
  170. Rotate((1.9078784028338913, -0.6000000000000001), θ) → R_3
  171. Segment(Q_3, R_3) → e7
  172. Rotate((1.3018071472837596, -0.26573027119611653), θ) → T_3
  173. Rotate((1.9595917942265424, -0.3999999999999999), θ) → U_3
  174. Segment(T_3, U_3) → e8
  175. Rotate((1.3219914074953556, -0.13286513559805826), θ) → V_3
  176. Rotate((1.98997487421324, -0.19999999999999996), θ) → W_3
  177. Segment(V_3, W_3) → e9
  178. Rotate((-0.5791456991917645, -1.1957862203825247), θ) → Z_3
  179. Rotate((-0.8717797887081344, -1.8), θ) → A_4
  180. Rotate((-0.7971908135883496, -1.0629210847844666), θ) → B_4
  181. Rotate((-1.1999999999999997, -1.6000000000000003), θ) → C_4
  182. Rotate((-0.9488468565221743, -0.9300559491864081), θ) → D_4
  183. Rotate((-1.4282856857085702, -1.4), θ) → E_4
  184. Rotate((-1.0629210847844666, -0.7971908135883498), θ) → F_4
  185. Rotate((-1.6, -1.2), θ) → G_4
  186. Rotate((-1.1506458270518265, -0.6643256779902914), θ) → H_4
  187. Rotate((-1.7320508075688774, -0.9999999999999999), θ) → I_4
  188. Rotate((-1.2177290821973479, -0.5314605423922332), θ) → J_4
  189. Rotate((-1.833030277982336, -0.7999999999999999), θ) → K_4
  190. Rotate((-1.2674526134856592, -0.3985954067941752), θ) → L_4
  191. Rotate((-1.907878402833891, -0.6000000000000004), θ) → M_4
  192. Rotate((-1.3018071472837596, -0.26573027119611686), θ) → O_4
  193. Rotate((-1.9595917942265424, -0.4000000000000004), θ) → P_4
  194. Rotate((-1.3219914074953556, -0.1328651355980584), θ) → Q_4
  195. Rotate((-1.98997487421324, -0.20000000000000015), θ) → R_4
  196. Segment(L_2, E_1) → g
  197. Segment(D_4, H_3) → h
  198. Segment(I_2, H_2) → l1
  199. Rotate(L, θ) → L'
  200. Rotate(M, θ) → M'
  201. Segment(L', M') → u1
  202. Segment(R_2, Q_2) → d5
  203. Segment(K_2, J_2) → d2
  204. Segment(M_2, L_2) → d3
  205. Segment(U_2, T_2) → d6
  206. Segment(W_2, V_2) → d7
  207. Segment(A_3, Z_2) → d8
  208. Segment(C_3, B_3) → d9
  209. Segment(R_4, Q_4) → g9
  210. Segment(P_4, O_4) → g8
  211. Segment(M_4, L_4) → g7
  212. Segment(K_4, J_4) → g6
  213. Segment(I_4, H_4) → g5
  214. Segment(G_4, F_4) → g4
  215. Segment(E_4, D_4) → g3
  216. Segment(C_4, B_4) → g2
  217. Segment(A_4, Z_3) → g1
  218. Rotate(L9, θ) → L99
  219. Rotate(L8, θ) → L88
  220. Segment(L88, L99) → i
  221. Rotate(L7, θ) → L77
  222. Point(Circle[L77, O2]) → P_2
  223. Segment(L77, P_2) → d11
  224. Segment(L77, O_2) → k
  225. Point(w) → T_4
  226. Point(xAxis) → U_4
  227. Vector(T_4, U_4) → z
  228. Rotate(L22, θ) → L2
  229. Segment(L2, M_2) → l
  230. Rotate(L11, θ) → L1
  231. Segment(F_1, L1) → n
  232. Point(d) → V_4
  233. CircleArc(V_4, L1, L2) → p
  234. Rotate(L33, θ) → L3
  235. Segment(L3, E_4) → q
  236. Rotate(L44, θ) → L4
  237. Segment(I_3, L4) → r
  238. CircleArc(V_4, L3, L4) → s
  239. Point(p) → W_4
  240. Point(s) → W_55
  241. Polygon(D_5, E_5, F_5, G_5) → poly2, d_5, e_5, f_5, g_5
  242. Polygon(H_5, I_5, J_5, K_5) → poly1, h_5, i_5, j_5, k_5