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9. Conside a dipole of dipole moment p oriented along the z-axis (see worksheet E-2, Problem 7 and the Challenge Problem for E-2 for further discussions of dipoles). b) Take the far-field approximation of this potential. That is, expand your answer to first order in d using the approximation (1+e)" - 1+ ne and then replacing qd with the dipole moment p. a) Modeling the dipole as two charges q separated by a distance d and centered on the origin, find the electric potential along the axis of the dipole a height z above the origin. Take the potential to be zero at infinity, i.e. V(z=0)=0. c) Find the z-component of the electric field along the z-axis. Compare your answer with the result found in E-2. d) Repeat parts (a) through (c), this time looking at points along the plane perpendicular to the dipole axis and intersecting the dipole, i.e. the z=0 plane.

9. Conside a dipole of dipole moment p oriented along the z-axis (see worksheet E-2, Problem 7 and the Challenge Problem for E-2 for further discussions of dipoles). b) Take the far-field approximation of this potential. That is, expand your answer to first order in d using the approximation (1+e)" - 1+ ne and then replacing qd with the dipole moment p. a) Modeling the dipole as two charges q separated by a distance d and centered on the origin, find the electric potential along the axis of the dipole a height z above the origin. Take the potential to be zero at infinity, i.e. V(z=0)=0. c) Find the z-component of the electric field along the z-axis. Compare your answer with the result found in E-2. d) Repeat parts (a) through (c), this time looking at points along the plane perpendicular to the dipole axis and intersecting the dipole, i.e. the z=0 plane.

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9. Conside a dipole of dipole moment p oriented along the z-axis (see worksheet E-2, Problem 7 and the Challenge Problem for E-2 for further discussions of dipoles). b) Take the far-field approximation of this potential. That is, expand your answer to first order in d using the approximation (1+c)" - 1+ ne and then replacing qd with the dipole moment p. a) Modeling the dipole as two charges q separated by a distance d and centered on the origin, find the electric potential along the axis of the dipole a height z above the origin. Take the potential to be zero at infinity, i.e. V(z=0)=0. c) Find the z-component of the electric field along the z-axis. Compare your answer with the result found in E-2. d) Repeat parts (a) through (c), this time looking at points along the plane perpendicular to the dipole axis and intersecting the dipole, i.o. the 2=0 plane. *
Transcribed Image Text:9. Conside a dipole of dipole moment p oriented along the z-axis (see worksheet E-2, Problem 7 and the Challenge Problem for E-2 for further discussions of dipoles). b) Take the far-field approximation of this potential. That is, expand your answer to first order in d using the approximation (1+c)" - 1+ ne and then replacing qd with the dipole moment p. a) Modeling the dipole as two charges q separated by a distance d and centered on the origin, find the electric potential along the axis of the dipole a height z above the origin. Take the potential to be zero at infinity, i.e. V(z=0)=0. c) Find the z-component of the electric field along the z-axis. Compare your answer with the result found in E-2. d) Repeat parts (a) through (c), this time looking at points along the plane perpendicular to the dipole axis and intersecting the dipole, i.o. the 2=0 plane. *
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