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A continuous line of charge of length \( 3 d \) lies along the \( x \)-axis, extending from \( x+d \) to \( x+4 d \). the line carries a uniform
\( \mathrm{P} \) linear charge density \( \lambda \)

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Figure \( 1.381 \)
In terms of \( d, \lambda \) and any necessary physical constants, find the magnitude of the electric field at the origin :
(A) \( \lambda / 5 \pi \varepsilon_{0} d \)
(B) \( \lambda / 4 \pi \varepsilon_{0} d \)
(C) \( 3 \lambda 16 \pi \varepsilon_{0} d \)
(D) \( 3 \lambda 8 \pi \varepsilon_{0} d \)
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