Question

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

This question was addressed to me in quiz.

My question comes from Cylindrical Coordinate System in section Coordinate Systems and Transforms of Electromagnetic Theory

Answer 1

Correct choice is (a) 2.467i + j + 1.167k

The best 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 = √(5^2+-2^2) = √29

sin θ = 5/√29 and cos θ = -2/√29

Thus, B = 2.467i + j + 1.167k.