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Q.

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/λ2 so that the field at O is along y direction.

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a

2

b

1.5

c

3

d

2.5

answer is A.

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Detailed Solution

Electric field due to semi-circular part: E2=λ22πε0RElectric 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/λ2 so that the field at O is along y direction.