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At a point in space the electric field components are Ex = -K*y, Ey = K*x, Ez = 0. Consider the statements: (I) the field is conservative; (II) the field is non-conservative; (III) the lines of force are straight lines; (IV) the lines of force are circles. Which combination is valid?

1. II and IV are valid
2. I and III are valid
3. I and IV are valid
4. II and III are valid

Correct answer: II and IV are valid

Solution

Curl_z = dEy/dx - dEx/dy = K - (-K) = 2K, which is nonzero, so the field is non-conservative (II valid, I invalid). The field vector (-Ky, Kx) is everywhere perpendicular to the position vector (x, y) and has constant magnitude on a circle, so the field lines are circles centred at the origin (IV valid, III invalid). Hence II and IV are correct.

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