KCET · Physics · Thermodynamics
Three point charges of \( +2 q,+2 q \) and \( -4 q \) are placed at the corners \( A, B \) and \( C \) of an equilateral triangle \( \mathrm{ABC} \) of side ' \( \mathrm{x} \) '. The magnitude of the electric dipole moment of this system is
- A \( 2 \) qx
- B \( 2 \sqrt{3} \) qx
- C \( 3 \sqrt{2} q x \)
- D \( 3 \mathrm{qx} \)
Answer & Solution
Correct Answer
(B) \( 2 \sqrt{3} \) qx
Step-by-step Solution
Detailed explanation
Net dipole moment
\(=\sqrt{4 p^{2}+4 p^{2}+2\left(4 p^{2}\right) \cos 60^{\circ}} \)
\(=\sqrt{4 p^{2}+4 p^{2}+8 p^{2} \times \frac{1}{2}} \)
\(=\sqrt{4 p^{2}+4 p^{2}+4 p^{2}}=\sqrt{12 p^{2}}=2 \sqrt{3} p\)
Therefore, net dipole moment \( 2 \sqrt{3} q x \)
\(=\sqrt{4 p^{2}+4 p^{2}+2\left(4 p^{2}\right) \cos 60^{\circ}} \)
\(=\sqrt{4 p^{2}+4 p^{2}+8 p^{2} \times \frac{1}{2}} \)
\(=\sqrt{4 p^{2}+4 p^{2}+4 p^{2}}=\sqrt{12 p^{2}}=2 \sqrt{3} p\)
Therefore, net dipole moment \( 2 \sqrt{3} q x \)
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