Torque and force on a dipole. An electric dipole is in a uniform external electric field E → as shown in Figure 17.52 . (a) What is the net force this field exerts on the dipole? (b) Find the orientations of the dipole for which the torque on it about an axis through its center perpendicular to the plane of the figure is zero, (c) Which of the orientations in part (b) is stable, and which is unstable? ( Hint: Consider a small displacement away from the equilibrium position, and see what happens.) (d) Show that, for the stable orientation in part (c), the dipole's own electric field opposes the external field for points between the charges. Figure 17.52 Problem 44.
Torque and force on a dipole. An electric dipole is in a uniform external electric field E → as shown in Figure 17.52 . (a) What is the net force this field exerts on the dipole? (b) Find the orientations of the dipole for which the torque on it about an axis through its center perpendicular to the plane of the figure is zero, (c) Which of the orientations in part (b) is stable, and which is unstable? ( Hint: Consider a small displacement away from the equilibrium position, and see what happens.) (d) Show that, for the stable orientation in part (c), the dipole's own electric field opposes the external field for points between the charges. Figure 17.52 Problem 44.
Torque and force on a dipole. An electric dipole is in a uniform external electric field
E
→
as shown in Figure 17.52. (a) What is the net force this field exerts on the dipole? (b) Find the orientations of the dipole for which the torque on it about an axis through its center perpendicular to the plane of the figure is zero, (c) Which of the orientations in part (b) is stable, and which is unstable? (Hint: Consider a small displacement away from the equilibrium position, and see what happens.) (d) Show that, for the stable orientation in part (c), the dipole's own electric field opposes the external field for points between the charges.
(a) Derive an expression for the electric field E due to a dipole of length ‘2a’ at a point distant r from the centre of the dipole on the axial line. (b) Draw a graph of E versus r for r >> a.
(c) If this dipole were kept in a uniform external electric field diagrammatically represent the position of the dipole in stable and unstable equilibrium and write the expressions for the torque acting on the dipole in both the cases.
Calculate the magnitude and direction of the dipole moment of the following arrangement of charges in the xy-plane: 3e at (0, 0), −e at (0.32 nm, 0), and −2e at an angle of 20° from the x-axis and a distance of 0.23 nm from the origin.
The following questions refer to the configuration
involving an electric dipole and an external
charged particle depicted below:
3. Suppose that the electric dipole has a length of
5 mm and the positive end has charge 8 nC. Let's
say that the external particle is 2 cm from both
ends of the dipole, carrying a charge of -2 µC.
What is the net electric force acting on the dipole?
[A positive net force points up, a negative one
points down.]
What is the net torque on the dipole relative to
its center point? [Positive torque implies
counterclockwise motion, negative implies
clockwise.]
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
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