UNIVERSITY OF TORONTO FACULTY OF APPLIED SCIENCE AND ENGINEERING Department of E
ID: 2267357 • Letter: U
Question
UNIVERSITY OF TORONTO FACULTY OF APPLIED SCIENCE AND ENGINEERING Department of Electrical and Computer Engineering UofT ECE 221H1S ELECTRIC AND MAGNETIC FIELDS VECTOR CALCULUS SELF-EVALUATION The following questions are based on vector calculus concepts that will be employed through the course. Please try them to identify your strengths and weaknesses and refer to Chapter 3 of the textbook for further study You do not need to hand in this test; it will not be graded. However, you are welcome to discuss these questions with your TAs and instructors. Q1. In which of the following coordinate systems, are all of the unit vectors independent of position? (a) Cartesian (b) Cylindrical (c) Spherical (d) None of the above Q2. What is the magnitude of the vector field E = r cos par + rz sin az at the point (x, y, z) = (-5,4,3)? (a) 13 (b) 5 (c) V50 (d) 4 (e)-16 Q3. What is the x-component of the vector field E = cos gar + rz sin az at the point (x, y,z)-(-5, 4, 3)? 20 (a) Ex =--Explanation / Answer
Answer:-1) Option (d) is correct. In spheriacal, out of three one is dependent on the position i.e. the radial distance, r . Rest two i.e. Phy and Theta are independent of position.
Answer:-2) Option (a) is correct. We can write rcos(phy) = x and rsin(phy) = y. Then magnitude of the vector is (x2 + (yz)2)0.5 = 13.
Answer:-3) Option (d) is correct. Since here in expression of E, second term related to phy is zero and we only have ar and az. Thus value of x-component is = r*cos2(phy).
where phy = tan-1(y/x) = -38.660. And r = ((-5)2+42) = (41)0.5 . Keeping all the values in r*cos2(phy) we get the result.
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