PHY 132 Lecture Notes - Lecture 3: Field Line, Electric Field

Which of the following statements are not true for electric field lines? 

(A) Electric field lines are close together in regions of space where the magnitude of the electric field is strong and are farther apart where it is weak.

(B) Electric field lines can never intersect.

(C) At every point in space, the electric field vector at that point is tangent to the electric field line through that point.

(D) Electric field lines are close together in regions of space where the magnitude of the electric field is weak and are farther apart where it is strong.

(E) Electric field lines point away from positive charges and toward negative charges.

(F) Electric field lines are continuous; they do not have a beginning or an ending.

(G) At every point in space, the electric field vector at that point is perpendicular to the electric field line through that point.

1. Electric field lines are drawn

(a) from positive charges to negative charges

(b) from negative charges to positive charges

(c) from the largest charge to the smallest charge

(d) from the smallest charge to the
largest charge.

2. The points where the potential is the same (in three-dimensional space) have the same voltage.
(a) True

(b) False

3. The points where the potential is the same (in three-dimensional space) lie on a surface.

(a) True
(b) False

4. The relationship between the direction of the electric field lines and the equipotential surfaces is
(a) field lines are everywhere parallel to surfaces

(b) field lines always intersect each other

(c) field lines are everywhere perpendicular to surfaces

(d) field lines always make angles between 08and 908
with surfaces.

Consider an electric dipole whose dipole moment (a vector pointing from the negative charge to the positive charge) is oriented at an angle  with respect to the y-axis. There is an external electric field of magnitude E  (independent of the field produced by the dipole) pointing in the positive y-direction. The positive and negative ends of the dipole have charges +q and -q, respectively, and the two charges are a distance d apart. The dipole has a moment of inertia I about its center of mass. It will help you to imagine that the dipole is free to rotate about a pivot through its center.

A) What is the net force   that the dipole experiences due to the electric field?

B) What is   , the magnitude of the torque that the electric field exerts about the center of mass of the dipole?

C) Using the above result, find the potential energy associated with the dipole's orientation in the field as a function of the angle    shown in the figure. Take the zero of the potential to occur when the dipole is at angle   ; that is  , .

D) In terms of the dipole moment   , What is the expression for the torque on a dipole in the field  ?

E) In terms of the dipole moment, What is the expression for the potential energy of a dipole in the field?