tailieunhanh - Ebook Bài tập Trường điện từ có lời giải

Ebook Bài tập Trường điện từ có lời giải sau đây nhằm giúp các bạn sinh viên có thêm tài liệu tham khảo, củng cố và rèn luyện kiến thức được học về Trường điện từ. | CHAPTER 1 . Given the vectors M 10ax 4ay 8az and N 8ax 7ay 2az find a a unit vector in the direction of M 2N. M 2N 10ax 4ay 8az 16ax 14ay 4az 26 10 4 Thus a 26 10 4 0-92 0-36 0-14 1 26 10 4 v ----- b the magnitude of 5ax N 3M 5 0 0 8 7 2 30 12 24 43 5 22 and 43 5 22 1 48-6. c M 2N M N 10 4 8 16 14 4 2 11 10 13-4 21-6 2 11 10 580-5 3193 2902 . Given three points A 4 3 2 B 2 0 5 and C 7 2 1 a Specify the vector A extending from the origin to the point A. A 4 3 2 4ax 3ay 2az b Give a unit vector extending from the origin to the midpoint of line AB. The vector from the origin to the midpoint is given by M 1 2 A B 1 2 4 2 3 0 2 5 1 1-5 3-5 The unit vector will be m 1 1-5 3-5 0-25 0-38 0-89 1 1-5 3-5 ---------------L c Calculate the length of the perimeter of triangle ABC Begin with AB 6 3 3 BC 9 2 4 CA 3 5 1 . Then AB BC CA 7-35 10-05 5-91 23-32 . The vector from the origin to the point A is given as 6 2 4 and the unit vector directed from the origin toward point B is 2 2 1 3. If points A and B are ten units apart find the coordinates of point B. With A 6 2 4 and B 1 B 2 2 1 we use the fact that B A 10 or 6 3 B ax 2 2 B ay 4 3 B az 10 Expanding obtain 36 8B 9 B2 4 8 B 9 B2 16 3 B 1B2 100 or B2 8B 44 0. Thus B 8 V64 176 11-75 taking positive option and so B I 11-75 ax I 11-75 ay 3 az 7-83ax 7-83ay 3-92az 1 . given points A 8 5 4 and B -2 3 2 find a the distance from A to B. B A 10 8 2 b a unit vector directed from A towards B . This is found through B A aAB IB - A -------------------- c a unit vector directed from the origin to the midpoint of the line AB. _ A B 2 aữM A B 2 3 -1 3 d the coordinates of the point on the line connecting A to B at which the line intersects the plane z 3. Note that the midpoint 3 -1 3 as determined from part c happens to have z coordinate of 3. This is the point we are looking for. . A vector field is specified as G 24xyax 12 x2 2 ay 18z2az. Given two points P 1 2 -1 and Q -2 1 3 .