1. The cylindrical coordinate system is also referred to as
a) Cartesian system
b) Circular system
c) Spherical system
d) Space system
Explanation: The cylindrical coordinates(r,φ,z) is also called as circular system and is used for systems with circular dimensions.
2. Transform the vector B=yi+(x+z)j located at point (-2,6,3) into cylindrical coordinates.
a) (6.325,-71.57,3)
b) (6.325,71.57,3)
c) (6.325,73.57,3)
d) (6.325,-73.57,3)
Explanation: ρ = √(x2+y2) = √40 = 6.325
Φ = tan-1(y/x) = tan-1(-6/2) = -71.57
z = 3.
3. Cylindrical systems have the following scalar values respectively
a) 1, ρ ,1
b) 1, 1, 1
c) 0,1,0
d) 1,0,0
Explanation: The range of radius is one to unity, that of plane angle is one to 360 degree and that of z plane is one to infinity. Thus the minimum scalar factor has to be 1, ρ , 1.
4. A charge located at point p (5,30⁰,2) is said to be in which coordinate system?
a) Cartesian system
b) Cylindrical system
c) Spherical system
d) Space system
Explanation: The cylindrical system is of the form (ρ, φ, z), which relates the point given in the question
5. Cylindrical system is employed in waveguides. State True/False.
a) True
b) False
Explanation: Cylindrical systems are employed in circular waveguides, whereas Cartesian systems are employed in rectangular waveguides.
6. The pressure inside a piston cylinder is a variable of
a) Radius
b) Plane angle
c) Z plane distance
d) Constant, not a variable
Explanation: Pressure varies up and down in a cylinder due to suction. Thus it is dependent on the z plane distance of the cylinder.
7. Charges filled inside a cylindrical will possess flux in which direction?
a) Upwards
b) Downwards
c) Laterally outwards
d) Inwards
Explanation: The flux due to the charges will act outside the cylinder. Since the cylinder possesses curved surfaces, it will flow laterally outwards.
8. Rectangular waveguides dominate the circular waveguides. Find the reason.
a) Low cut-off frequency
b) Easy to design
c) More wave propagation
d) The statement is false
Explanation: Due to linear design, the desired dimensions can be easily constructed using rectangular waveguides than circular ones
9. Transform the spherical system B = (10/r)i + (10cos θ)j + k into cylindrical form at (5, π/2, -2)
a) 2.467i + j + 1.167k
b) 2.467i – j + 1.167k
c) 2.467i – j – 1.167k
d) 2.467i + j – 1.167k
Explanation: The equivalent cylindrical form is given by,
B = (10sin θ/r + rcos2θ)i + j + (10cos θ/r –r sin θ cos θ)k
At (5, π/2, -2), r = √(52+-22) = √29
sin θ = 5/√29 and cos θ = -2/√29
Thus, B = 2.467i + j + 1.167k.
10. Convert the given rectangular coordinates A(2,3,1) into corresponding cylindrical coordinates
a) (3.21,56.31,1)
b) (3.21,57.31,0)
c) (3.61,57.31,0)
d) (3.61,56.31,1)
Explanation: ρ = √(x2+y2) = √13 = 3.61
Φ = tan-1(y/x) = 56.31
z = 1
Thus, A = (3.61,56.31,1).