Consider an electric field with components Eₓ = -Ky, Eᵧ = Kx, and zero z-component. (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 conclusions are valid?
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Question

Consider an electric field with components Eₓ = -Ky, Eᵧ = Kx, and zero z-component. (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 conclusions are valid?

Options

G1 Physics · Accepted Answer

For a conservative field, ∂Eᵧ/∂x must equal ∂Eₓ/∂y. Here ∂Eᵧ/∂x = K while ∂Eₓ/∂y = −K, so the field is non-conservative. Field lines satisfy dy/dx = Eᵧ/Eₓ = −x/y, giving x² + y² = constant, i.e. circles. Therefore II and IV are valid. Correct answer: A.

Consider an electric field with components Eₓ = −Ky, Eᵧ = Kx, and zero z-component. (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 conclusions are valid?