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Question: An electric field of 1000 V/m is applied to an electric dipole at angle of 45°. The value of electri...

An electric field of 1000 V/m is applied to an electric dipole at angle of 45°. The value of electric dipole moment is 10−2910^{-29} C.m. What is the potential energy of the electric dipole?

A
  • 7 × 10−2710^{-27} J
B
  • 20 × 10−1810^{-18} J
C
  • 9 × 10−2010^{-20} J
D
  • 10 × 10−2910^{-29} J
Answer

-7 × 10−2710^{-27} J

Explanation

Solution

The potential energy UU of an electric dipole with dipole moment p⃗\vec{p} in a uniform electric field E⃗\vec{E} is given by:

U=−p⃗⋅E⃗=−pEcos⁡θU = -\vec{p} \cdot \vec{E} = -pE \cos \theta

Given:

  • E=1000 V/mE = 1000 \, V/m
  • p=10−29 C⋅mp = 10^{-29} \, C \cdot m
  • θ=45∘\theta = 45^\circ

Substitute the values:

U=−(10−29 C⋅m)×(1000 V/m)×cos⁡(45∘)U = -(10^{-29} \, C \cdot m) \times (1000 \, V/m) \times \cos(45^\circ)

U=−10−26 J×12U = -10^{-26} \, J \times \frac{1}{\sqrt{2}}

U≈−7.07×10−27 J≈−7×10−27 JU \approx -7.07 \times 10^{-27} \, J \approx -7 \times 10^{-27} \, J