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Unformatted text preview: Q1. a) Given = + + where a, b, c are constants. Is A a constant vector? Find the cylindrical and spherical components of A, expressing them in terms of ρ, φ, z and r, θ, φ, respectively. b) Given = + + where a, b, c are constants. Is A a constant vector? Find i) ∙ ii) ∇ × . Find the rectangular and spherical components of A, expressing them in terms of x, y, z and r, θ, φ, respectively. Q2. Given a vector function F = ax(x + c1z) + ay(c2x – 3z) + az(x + c3y + c4z). a) Determine the constants c1, c2, and c3 if F is conservative. b) Determine the constant c4 if F is also solenoidal. c) Determine the scalar potential function V whose negative gradient equals F. Given a vector function E = axy + ayx, evaluate the scalar line integral ∫E·dl from P1(2, 1, –1) to P2(8, 2, –1) a) along the parabola x = 2y2, b) along the straight line joining the two points Is this E a conservative field? Q3. Q4. Four point charges, q1= q2= q3= q4=30 µC, are located at (4, 0, 0), (0, 4, 0), (4, 0, 0) and (0, 4, 0), respectively (in Cartesian coordinate system). Find the total force on the charge q0=150 µC which is placed at (0, 0, 3).
z q0 q4 q3 q1
x q2 y Q5. A line charge of uniform density ρℓ in free space forms a semicircle of radius b. Determine the magnitude and direction of the electric field intensity at the center of the semicircle. ρℓ
b x Q6. Two point charges, Q1 and Q2, are located at (1, 2, 0) and (2, 0, 0), respectively. Find the P(1,1,0) relation between Q1 and Q2 such that the total force on a test charge at P(2, 0, 0) will have; (a) No xcomponent (b) No ycomponent ...
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 Spring '10
 Liu

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