Question 896: Electrostats & Capacitance

Question

An electric dipole with dipole moment $5 	imes 10^{-6} \mathrm{Cm}$ is aligned with the direction of a uniform electric field of magnitude $4 	imes 10^5 \mathrm{~N} / \mathrm{C}$. The dipole is then rotated through an angle of $60^{\circ}$ with respect to the electric field. The change in the potential energy of the dipole is:

Accepted Answer

Given:
Dipole moment, $ |\vec{P}| = 5 	imes 10^{-6} \, 	ext{Cm} $
Electric field magnitude, $ |\vec{E}| = 4 	imes 10^5 \, 	ext{N/C} $
Initial angle, $ 	heta_i = 0^\circ $
Final angle, $ 	heta_f = 60^\circ $
To calculate the change in potential energy $ \Delta U $ of the dipole:
$ \Delta U = U_f - U_i = -PE \cos 	heta_f + PE \cos 	heta_i $
Simplifying, we have:
$ \Delta U = PE \left( \cos 	heta_i - \cos 	heta_f ight) $
Substitute the known values:
$ \Delta U = 5 	imes 10^{-6} 	imes 4 	imes 10^5 \left(1 - \frac{1}{2}ight) $
Calculate further:
$ \Delta U = 5 	imes 10^{-6} 	imes 4 	imes 10^5 	imes \frac{1}{2} $
$ \Delta U = 10 	imes 10^{-6} 	imes 10^5 $
Which simplifies to:
$ \Delta U = 1 \, 	ext{J} $
Thus, the change in the potential energy of the dipole is $\boxed{1 \, 	ext{J}}$.

Answer

1.2 J

Answer

1.5 J

Answer

0.8 J

Answer

1.0 J

Electrostats & Capacitance

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