Tutorial#0Problems,ECE3336,Winter2026
Problem #1
Find the area of a cylindrical surface described by r = 5, 30◦ ≤ ϕ ≤ 60◦ , and
0 ≤ z ≤ 3.
Problem #2
The spherical strip shown is a section of a
sphere of radius 3 [cm]. Find the area of the
strip.
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Problem #3
A circular cylinder of radius r = 5 [cm] is concentric with the z-axis and extends between
z = −3 [cm] and z = 3 [cm]. Use Eq. (1) to find the cylinder’s volume.
dv = rdrdϕdz
(1)
Problem #4
A sphere of radius 2 [cm] contains a volume charge density ρv given by
ρv = 4 cos2 θ [C/m3 ]
(2)
Find the total charge Q contained in the sphere.
Problem #5
Find the gradient of each of the following scalar functions and then evaluate it at the given
point.
(a) V1 = 24V0 cos(πy/3)sin(2πz/3) at (3, 2, 1) in Cartesian coordinates.
(b) V2 = V0 e−2r sin(3ϕ) at (1, π/2, 3) in cylindrical coordinates.
(c) V3 = V0 (a/r) cos(2θ) at (2a, 0, π) in spherical coordinates.
Problem #6
Given A, find ∇ · A.
x̂ sin(2x) + ŷ cos(2x)) in Cartesian coordinates.
(a) A1 = e−2y (x̂
(b) A2 = r̂r̂r cos ϕ + ϕ̂
ϕ̂r sin ϕ + ẑẑ3z in cylindrical coordinates.
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Problem #7
Given A, find ∇ × A.
(a) A1 = r̂r̂10e−2r cos ϕ + ẑẑ10 sin ϕ at (2, 0, 3) in cylindrical coordinates.
(b) A2 = θ̂θ̂12 sin θ at (3, π/6, 0) in spherical coordinates.
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