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A particle is placed in a field characterized by a value of gravitational potential given by \( V=-k x y \), where \( k \) is a constant. If \( \vec{E}_{g} \) is the gravitational field then,
(A) \( \vec{E}_{g}=k(x \hat{i}+y \hat{\boldsymbol{j}}) \) and is conservative in nature
(B) \( \vec{E}_{g}=k(y \hat{i}+x \hat{j}) \) and is conservative in nature
(C) \( \vec{E}_{g}=k(x \hat{i}+-y \hat{j}) \) and is non-conservative in nature
(D) \( \overrightarrow{\boldsymbol{E}}_{g}=k(y \hat{i}+x \hat{j}) \) and is non-conservative in nature
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