A point charge of +35 nC is above a point charge of –35 nC on a vertical line. The distance between the charges is 4.0 mm. What are the magnitude and direction of the dipole moment ?

Magnitude = 140 x 10⁻¹² Cm

Direction = upwards

Explanation:

A pair of two equal and opposite point charges forms an electric dipole.

The magnitude of the moment of such dipole is the product of the magnitude of any of the charges (since the charges are the same in magnitude) and the distance of separation between them. i.e

p = q x d          (i)

Where;

p = dipole moment

q = magnitude of any of the charges

d = distance between the charges.

The direction of the dipole moment is from the negative charge to the positive charge.

(a) From the question, the charges are +35 nC and -35 nC, and the distance between them is 4.00mm.

This implies that;

q = 35 nC = 35 x 10⁻⁹C

d = 4.00mm = 4.0 x 10⁻³ m

Substitute the values of q and d into equation (i) to give;

p = 35 x 10⁻⁹C x 4.00 x 10⁻³ m

p = (35 x 4.0) x (10⁻⁹ x 10⁻³) C m

p = 140 x 10⁻¹² Cm

The magnitude of the dipole moment is 140 x 10⁻¹² Cm

(b) From the question, the +35nC charge is above the -35nC charge on a vertical line as shown below;

                         o   +35nC

                          |

                          |

                          |

                          |

                          |

                          |

                         o    -35nC

Since the direction should point from the negative charge to the positive charge, this means that the direction of the dipole moment of the two charges is upwards (due North).

                         o   +35nC

                         ↑

                          |

                          |

                          |

                          |

                          |

                          |

                         o    -35nC