An electric dipole with dipole moment P = ($2.54 imes 10^{-28}$ C...

Question

An electric dipole with dipole moment P = ($2.54 	imes 10^{-28}$ C.m) (2.00 î + 3.00 j ) is placed in an electric field E = 1000 î . An external agent turns the dipole until its electric dipole moment is P = ($2.54 	imes 10^{-28}$ C.m) (− 3.00 î + 2.00 ĵ ). The work done by the agent is :

Accepted Answer

Work done by external agent $=\Delta U = U_f - U_i = (-\vec p_f\cdot\vec E)-(-\vec p_i\cdot\vec E)=\vec p_i\cdot\vec E-\vec p_f\cdot\vec E$

Given $\vec E=1000\hat i$ N/C (only x-component matters for the dot product):

$\vec p_i\cdot\vec E = (2.54\times10^{-28}\times2.00)\times1000=5.08\times10^{-25}$ J

$\vec p_f\cdot\vec E = (2.54\times10^{-28}\times(-3.00))\times1000=-7.62\times10^{-25}$ J

$$W=5.08\times10^{-25}-(-7.62\times10^{-25})=12.7\times10^{-25}=1.27\times10^{-24}\text{ J}$$

Answer: (B) $1.27\times10^{-24}$ J

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