Question

Given B= (10/r)i+( rcos θ) j+k in spherical coordinates. Find Cartesian points at (-3,4,0)

(a) -2i + j

(b) 2i + k

(c) i + 2j

(d) –i – 2k

The question was posed to me during an online exam.

The query is from Spherical Coordinate System topic in section Coordinate Systems and Transforms of Electromagnetic Theory

Answer 1

Correct option is (a) -2i + j

Explanation: r = √(x^2+y^2+z^2) = √25 = 5

Θ = cos^-1(z/r) = 1

Φ = tan^-1(y/x) = tan^-1(-4/3)

Thus, B = -2i + j.