Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 28 - The Electric Potential - Conceptual Questions - Page 832: 5

Answer

$$U_{a}\gt U_{c }\gt U_{e }=U_{f}\gt U_{b }\gt U_{d }$$

Work Step by Step

We know that the electric potential of a dipole is given by $$U_{\rm dipole}=-pE\cos\phi$$ Hence, the electric potentials of the given dipole are as follows: $$U_{a,\rm dipole}=-pE\cos180^\circ= +pE$$ $$U_{b,\rm dipole}=-pE\cos 45^\circ= -0.707pE$$ $$U_{c,\rm dipole}=-pE\cos 135^\circ= +0.707pE$$ $$U_{d,\rm dipole}=-pE\cos 0^\circ=-pE$$ $$U_{e,\rm dipole}=-pE\cos 90^\circ=0$$ $$U_{f,\rm dipole}=-pE\cos 270^\circ=0$$ Ranking from most positive to most negative, $$\boxed{U_{a,\rm dipole}\gt U_{c,\rm dipole}\gt U_{e,\rm dipole}=U_{f,\rm dipole}\gt U_{b,\rm dipole}\gt U_{d,\rm dipole}}$$
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