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Mời các bạn tham khảo tài liệu Giải bài tập Trường điện từ sau đây để biết được các dạng bài tập chính cũng như nắm bắt những kiến thức lý thuyết và công thức tính về trường điện từ thông qua việc giải những bài tập trong tài liệu. | CHAPTER 1 1.1. Given the vectors M 10a 4ay 8a and N 8a 7ay 2a find a a unit vector in the direction of M 2N. M 2N 10a. 4ay 8a 16a. 14ay 4a 26 10 4 Thus 26 10 4 a 1 26710 0-92-0-36-a14 b the magnitude of 5a N 3M 5 0 0 8 7 2 30 12 24 43 5 22 and 1 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 1.2. The three vertices of a triangle are located at A 1 2 5 B 4 2 3 and C 1 3 2 . a Find the length of the perimeter of the triangle Begin with AB 3 4 8 BC 5 5 1 and CA 2 1 7 . Then the perimeter will be Ề AB bC CA X 9 16 64 725 25 1 74 1 49 23 9. b Find a unit vector that is directed from the midpoint of the side AB to the midpoint of side BC The vector from the origin to the midpoint of AB is M . 2 A B 1 5a 2a . The vector from the origin to the midpoint of BC is M v. 2 B C 2 3a ay 5a . The vector from midpoint to midpoint is now Mas Mbc 2 2a ay 7a . The unit vector is therefore Ma_b Mso 2a a 7a -mm .7 KA I ay-- 0.27a 0.14ay 0.95a Mas Mbc 7.35 where factors of 1 2 have cancelled. c Show that this unit vector multiplied by a scalar is equal to the vector from A to C and that the unit vector is therefore parallel to AC. First we find AC 2a ay 7a which we recognize as 7.35aMM. The vectors are thus parallel but oppositely-directed . 1.3. 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 3B 2 2 1 we use the fact that B A 10 or 6 3 B a 2 3 B ay 4 3 B a 10 Expanding obtain 36 8B 9 B3 4 8 B 4 B3 16 8 B 9 B3 100 or B3 8B 44 0. Thus B 8 V64 176 11.75 taking positive option and so B 2 11.75 a 11.75 ay j 11.75 a 7.83a 7.83ay 3.92a 3 3 3 1 1.4. A circle centered at the origin with a radius of 2 units lies in the xy plane. Determine the unit vector in rectangular components that lies in the xy plane is tangent to the circle at y 3 1 0 and is in the general direction of increasing .
