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Chapter 16: Q49P (page 626)

A dipole is oriented along the x axis. The dipole moment is p=(qs).

(a) Calculate exactly the potential V(relative to infinity) at a location {x,0,0}on the xaxis and at a location {0,y,0}on the yaxis, by superposition of the individual 1/rcontributions to the potential.

(b) What are the approximate values of Vat the locations in part (a) if these locations are far from the dipole?

(c) Using the approximate results of part (b), calculate the gradient of the potential along the xaxis, and show that the negative gradient is equal to the x component Ex of the electric field.

(d) Along the y axis, dV/dy=0. Why isn鈥檛 this equal to the magnitude of the electric field Ealong the yaxis?

Short Answer

Expert verified

It is showed that the gradient along yaxis is not equal to the magnitude of the electric field Ealong they axis.

Step by step solution

01

Write the given data from the question.

The dipole is oriented along the xaxis.

The dipole, p=qs

Along the y axis, dV/dy=0.

02

Determine the formulas to calculate the potential and gradient of the potential.

The expression to calculate the potential at the location is given as follows.

V=14蟺蔚0qr鈫�

Here,r鈫� is the relative position vector.

03

Along the y axis, dV/dy=0. Why isn’t this equal to the magnitude of the electric field Ealong the y axis.

Since the potential along the yaxis is zero. Therefore, the gradient of the potential along the yis also zero and the gradient along axis is not equal to the magnitude of the electric field Ealong the yaxis.

Hence it is showed that the gradient along yaxis is not equal to the magnitude of the electric field Ealong they axis.

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Most popular questions from this chapter

In a region with an uniform electric field, you measure a potential difference of from the origin to a position of (0,0,10) m. Now we add a uniformly charged, thin spherical plastic shell centered at the origin. The spherical shell has a radius of 5 m and a charge of -3530 nC. Draw a diagram to help answer the following questions: (a) What is the potential difference from the origin to a position of (0,0,5) m (at the surface of the spherical shell)? (b) What is the potential difference from the position of (0,0,5) m to a position of (0,0,10) m ?

A dipole is centered at the origin, with its axis along the y axis, so that at locations on the y axis, the electric field due to the dipole is given by

E鈫�=鉄�0,鈥�14蟺蔚02qsy3,鈥�0鉄�鈥�Vm

The charges making up the dipole are+3鈥塶颁 and -3鈥塶颁, and the dipole separation is2鈥尘尘 (Figure 16.82). What is the potential difference along a path starting at location鉄�0,鈥�0.03,鈥�0鉄�鈥尘 and ending at location鉄�0,鈥�0.04,鈥�0鉄�鈥尘 ?

Question: In Chapter 6 we saw that the electric potential energy of a system of two particles is given by the equation Uel=14蟺蔚0q1q2r.

(a) What is the electric potential energy of two protons separated by a distance of 9nm9脳10-9m? (b) What is the electric potential energy of a proton and an electron separated by the same distance?

Locations A and B are in a region of uniform electric field, as shown in Figure 16.67. Along a path from B to A, the change in potential is-2200V. The distance from A to B is 0.28m. What is the magnitude of the electric field in this region?

An electron starts from rest in a vacuum, in a region of strong field. The electron moves through a potential difference of 44V. (a) What is the kinetic energy of the electron in electron volts (eV)? (b) Which of the following statements would be true if the particle were a proton? Choose both if they are both correct. (1) The kinetic energy of the proton would be negative. (2) The proton would move in the opposite direction from the electron.
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