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An electric field in a region of space is given by Ex = -K*y, Ey = K*x, Ez = 0 (where K is a positive constant). Four statements about this field are made: (I) The field is conservative. (II) The field is non-conservative. (III) The field lines are straight lines. (IV) The field lines are circles. Which combination of statements is correct?

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

Since curl E = 2K (not zero), the field is non-conservative. The field line differential equation dx/(-Ky) = dy/(Kx) gives x*dx + y*dy = 0, integrating to x² + y² = const (circles centred at the origin).

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