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Attributed to the lack of an Earth-like global intrinsic dipole magnetic field on Mars, the induced electromagnetic field environment plays a crucial role in the evolution of its atmosphere. The dominant motional electric field (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="bold-italic">E</mi></mrow><mrow><mi mathvariant="bold-italic">M</mi></mrow></msub></mrow></semantics></math></inline-formula>) induced by the bulk motion of the magnetic field within the Martian magnetosheath serves to accelerate ions toward escape velocity, thereby forming a plume escape channel. However, the distribution morphology of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="bold-italic">E</mi></mrow><mrow><mi mathvariant="bold-italic">M</mi></mrow></msub></mrow></semantics></math></inline-formula> itself has received limited attention in previous research. In this study, by taking advantage of the multi-fluid Hall-MHD model cooperating with the Martian crustal field model, we focus on elucidating the physical mechanisms underlying the asymmetrical distribution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="bold-italic">E</mi></mrow><mrow><mi mathvariant="bold-italic">M</mi></mrow></msub></mrow></semantics></math></inline-formula> and examining the influence of the crustal field on this asymmetry. The results obtained from the simulation conducted in the absence of the crustal field indicate that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="bold-italic">E</mi></mrow><mrow><mi mathvariant="bold-italic">M</mi></mrow></msub></mrow></semantics></math></inline-formula> is more intense within the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mo>−</mo><mi>Z</mi></mrow><mrow><mi>M</mi><mi>S</mi><mi>E</mi></mrow></msub></mrow></semantics></math></inline-formula> magnetosheath, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="bold-italic">E</mi></mrow><mrow><mi mathvariant="bold-italic">M</mi></mrow></msub></mrow></semantics></math></inline-formula> is directed toward Mars, primarily due to its corresponding higher velocity and a stronger magnetic field at lower solar zenith angles. The Martian crustal field has the ability to enhance the local <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="bold-italic">E</mi></mrow><mrow><mi mathvariant="bold-italic">M</mi></mrow></msub></mrow></semantics></math></inline-formula> around the inner boundary of the magnetosheath by amplifying both the magnetic field and its associated velocity. Accordingly, these findings provide valuable insights into the asymmetric nature of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="bold-italic">E</mi></mrow><mrow><mi mathvariant="bold-italic">M</mi></mrow></msub></mrow></semantics></math></inline-formula> within the Martian magnetosheath under typical quiet-time solar wind conditions.