The correct option is (B) \(41 .\)
Explanation:
$$
\mathrm{I}_{\mathrm{A}}=\mathrm{I}_{1}+\mathrm{I}_{2}+2 \sqrt{\left(\mathrm{I}_{1} \mathrm{I}_{2}\right) \cos \phi}
$$
At point \(\left.A, I_{A}=1+4 I+2 \sqrt{(I} \times 4 I\right) \cos (\pi / 2)=5 I+0=5 I\)
At point \(\left.B, I_{B}=|+4|+2 \sqrt{(}|\times 4|\right) \cos \pi\)
$$
\begin{aligned}
&=5 \mathrm{I}+(2 \times 2 \mathrm{l} \times-1) \\
&=5 \mathrm{I}-4 \mathrm{I}=\mathrm{I} \\
&\mathrm{I}_{\mathrm{A}}-\mathrm{I}_{\mathrm{B}}=5 \mathrm{I}-\mathrm{I}=4 \mathrm{I}
\end{aligned}
$$
i.e. difference between intensities \(=41\)
