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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 x-component (b) No y-component ...
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- Spring '10