Three charges are arranged on the vertices of a right angle triangle as shown in the figure. The magnitude of dipole moment of the combination in the unit of C-cm is

• A

  $10 \sqrt{2} \mathrm{q}$
• B

  $5 \mathrm{q}$
• C

  $5 \mathrm{q}$
• Correct answer
  D

  $10 \mathrm{q}$

Solution

Let side of $\mathrm{AB}$ and $\mathrm{BC}$ is a $$ \begin{aligned} & \mathrm{a}^2+\mathrm{a}^2=(10)^2 \mathrm{~cm} \\ & 2 \mathrm{a}^2=(10)^2 \\ & \mathrm{a}=\frac{10}{\sqrt{2}} \end{aligned} $$ The magnitude of dipole moment $$ \begin{aligned} & P=2 q a \cos \theta=2 q \times \frac{10}{\sqrt{2}} \times \cos 45 \\ & =2 \varepsilon \times \frac{10}{\sqrt{2}} \times \frac{1}{\sqrt{2}}=10 \mathrm{~cm} \end{aligned} $$

Hence, the correct answer is option: 'D'.