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In the figure shown, find the ratio of the linear charge densities λ1 (on semi-infinite straight wire) and λ2 (on semi-circular part) that is λ1/λ2so that the field at O is along y-direction.

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answer is 2.

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Detailed Solution

Electric field due to semicircular part:E2=λ22πε0R Electric field due to straight part:E1x=E1y=λ14πε0RFor net field to be along y-axis:E2=E1x⇒λ22πε0R=λ14πε0R⇒λ1λ2=2

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In the figure shown, find the ratio of the linear charge densities λ1 (on semi-infinite straight wire) and λ2 (on semi-circular part) that is λ1/λ2so that the field at O is along y-direction.