Answer to Question #134283 in Electricity and Magnetism for Rohan

Question

If the z-axis is vertical and ŝ, φ̂, ẑ are unit vectors in cylindrical coordinates (standard symbols),

(a) ŝ is horizontal

(b) φ̂ is horizontal

(c) φ̂ is vertical

(d) ŝ is vertical

(Note:- This question have one or more than one correct choice(s) out of the four given choices. Any number of options may be correct.)

Answer 1

Let us consider the cylindrical coordinate system. In such a system ŝ denotes a unit vector along the radius, so it is situated in the plane perpendicular to z-axis and in is horizontal (so (a) is true and (d) is false)

φ̂ is a unit vector related to azimuth, so it's also in the plane perpendicular to z-axis and it's horizontal. Therefore, (b) is true and (c) is false.