A simple electric dipole consists of a positive and negative charge of equal magnitude held very close to one another. The component of the electric field pointing away from a dipole has magnitude
E =,
where d is the distance from the center of the dipole to the point in question, k = 9.0 x 109 N.m2/C2 is a universal constant, and p is the magnitude of the dipole moment vector, which specifies the strength and direction of the dipole. Here, q denotes the angle between the dipole moment vector and d, the displacement vector (from the dipole to the point in question).
A student performs an experiment to determine if a mystery object is an electric dipole. (The mystery object is only a few millimeters long.) Using a sophisticated instrument, the student measures the component of the electric field pointing away from the object, at various distances from the center of the object. By taking each measurement along an imaginary line emanating outward from the center of the mystery object, he ensures that “q ” stays the same throughout the experiment. Table 1 shows the electric field he found at various distances.
TABLE 1

Trial | distance (m) | field (N/C) |

1 | 0.010 | 3.6 10-10 |

2 | 0.020 | 9.0 10-11 |

3 | 0.030 | 4.0 10-11 |

1. | Assuming the data is free from major errors, what can the student conclude about the mystery object? I. It might be a dipole. II. It might be (approximately) a point charge.

A. | I only

B. | II only

C. | Both I and II

D. | Neither I nor II

2. | From the given information, can we calculate the electrostatic force that would act on a point charge q = 2.5 10-7 C, held at the location where the student measured the electric field in trial 2?

A. | Yes, because we can use F =, with r = 0.02 m.

B. | Yes, because we know the electric field at the relevant point.

C. | No, because the formula F = doesn't apply, and we don't know the dipole moment.

D. | No, because even though F = applies, we don't know both q1 and q2.

3. | Which of these graphs best expresses how the electric field measured by the student varies with distance from the mystery object?

A. |

B. |

C. |

D. |

4. | Consider the electric field produced by a dipole. If the dipole moment and the distance from the dipole are both doubled, while q is kept the same, the electric field component pointing away from the dipole decreases by a factor of:

A. | 2

B. | 4

C. | 8

D. | 16

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