Problem

$\bullet$ $\bullet$ (a) An electron is moving eas…

03:55

Problem 45 Hard Difficulty

$\bullet$ $\bullet$ Torque and force on a
dipole. An electric dipole is in
a uniform external electric field
$\vec{E}$ as shown in Figure 17.49 .
(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 dis-
placement 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.

Answer

a) zero
b) When the length vector from $-q$ to $+q$ is parallel $(=0)$
c) If the length vector from $-q$ to $+q$ is parallel to $\overline{E}$ , then the orientation is stable, and if the length vector from $-q$ to $+q$ is antiparallel to $\overline{E}$ then the orientation is unstable.
d) So, the electric field due to the dipole is directed from the $+q$ charge to the $-q$ charge which is opposite to the external electric field, as shown in the figure.

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Physics 102 Electricity and Magnetism

College Physics

Chapter 17

Electric Charge and Electric Field

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Video Transcript

problem Number 45. In this problem, our die Paul is situated and then external electric field. This is extremely electric Field e and our Dybul, it's I'll ask you and mine. Sq Charge is situated in the electric field at an angle with the electric field. No. In the first part of the question, we have to find that net force on the double. We know that positive charge in an external electric field experiences a force in their direction off the electric field. So the force on the plus que chart is in the right direction and the four Sunda mine sq charge is in the left direction because negative charge feels the force oppose it to the external electric field. These two forces directing on the DIA pull in the opposite directions. So the net force on that die pull not force on That I pull is equal to zero. Now in the party, we have to find the dark on their die. Pull Venda dark on the double zero. No, Ben, The dark on the double is given us the force that big on their Di Poole. The stands between the force and the access are and, uh, angle between the two, which is signed treater when dorky zero, then sign Rita should also be Jiro. This implies that treater is equal to zero degrees does when force and the line connecting that two charges our peddler, then that dark wonder die Paul is zero. This can be grown iss. This is a rescue and this is minus Q when the angle between the this stance victor and the fourth sector zero than that or Kanda that bull is zero. Now, for the hard part of the question, we have to find the is stable and on a stable position off their Di Poole. The stable position is this vendor Dapple is making zero needy good, uh, electric field. And the on the stable position is this when that apple is making 1 80 degrees with, uh electric field in the stable position, the electric field is dedicated towards star mine sq charge from the flask. You judge, this is dialectics. Field off their Di Poole and the external electric field is oppose it too. This electric field, so in a stable condition, the electric field will point from plus two plus Q minus. Q

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