An electric dipole moment vec{p} = (2.0hat{i} | vedclass

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(D) Given: $\vec{p} = (2.0\hat{i} + 3.0\hat{j}) 	imes 10^{-6} 	ext{ C m}$ and $\vec{E} = (3.0\hat{i} + 2.0\hat{k}) 	imes 10^{5} 	ext{ N C}^{-1}$.$

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All of the above.

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(D) Given: $\vec{p} = (2.0\hat{i} + 3.0\hat{j}) 	imes 10^{-6} 	ext{ C m}$ and $\vec{E} = (3.0\hat{i} + 2.0\hat{k}) 	imes 10^{5} 	ext{ N C}^{-1}$.$1$. Torque $\vec{	au} = \vec{p} 	imes \vec{E} = (2.0\hat{i} + 3.0\hat{j}) 	imes 10^{-6} 	imes (3.0\hat{i} + 2.0\hat{k}) 	imes 10^{5}$.$\vec{	au} = 10^{-1} 	imes [ (2.0\hat{i} 	imes 3.0\hat{i}) + (2.0\hat{i} 	imes 2.0\hat{k}) + (3.0\hat{j} 	imes 3.0\hat{i}) + (3.0\hat{j} 	imes 2.0\hat{k}) ]$.Using cross products: $\hat{i} 	imes \hat{i} = 0, \hat{i} 	imes \hat{k} = -\hat{j}, \hat{j} 	imes \hat{i} = -\hat{k}, \hat{j} 	imes \hat{k} = \hat{i}$.$\vec{	au} = 0.1 	imes [ 0 - 4.0\hat{j} - 9.0\hat{k} + 6.0\hat{i} ] = (0.6\hat{i} - 0.4\hat{j} - 0.9\hat{k}) 	ext{ Nm}$. Statement $(A)$ is correct.$2$. Potential Energy $U = -\vec{p} \cdot \vec{E} = - [ (2.0\hat{i} + 3.0\hat{j}) 	imes 10^{-6} \cdot (3.0\hat{i} + 2.0\hat{k}) 	imes 10^{5} ]$.$U = -0.1 	imes [ (2.0 	imes 3.0) + (3.0 	imes 0) ] = -0.6 	ext{ J}$. Statement $(B)$ is correct.$3$. Maximum potential energy $U_{	ext{max}} = |\vec{p}| |\vec{E}|$.$|\vec{p}| = \sqrt{2.0^2 + 3.0^2} 	imes 10^{-6} = \sqrt{13} 	imes 10^{-6} 	ext{ C m}$.$|\vec{E}| = \sqrt{3.0^2 + 2.0^2} 	imes 10^{5} = \sqrt{13} 	imes 10^{5} 	ext{ N C}^{-1}$.$U_{	ext{max}} = \sqrt{13} 	imes 10^{-6} 	imes \sqrt{13} 	imes 10^{5} = 13 	imes 10^{-1} = 1.3 	ext{ J}$. Statement $(C)$ is correct.Since all statements are correct,the answer is $(D)$.

An electric dipole moment $\vec{p} = (2.0\hat{i} + 3.0\hat{j}) \times 10^{-6} \text{ C m}$ is placed in a uniform electric field $\vec{E} = (3.0\hat{i} + 2.0\hat{k}) \times 10^{5} \text{ N C}^{-1}$. Which of the following statements is correct?

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