Q. 77

Expert-verifiedFound in: Page 628

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

In Section we claimed that a charged object exerts a net attractive force on an electric dipole. Let’s investigate this. *FIGURE CP22.77* shows a permanent electric dipole consisting of charges +q and -q separated by the fixed distance s. Charge *+Q* is the distance r from the center of the dipole. We’ll assume, as is usually the case in practice, that s *V r. *

a. Write an expression for the net force exerted on the dipole by charge *+Q.*

b. Is this force toward *+Q* or away from *+Q?* Explain.

c. Use the binomial approximation *nx* if *x V 1* to show that your expression from part a can be written *Fnet = 2KqQs/r3 . *

d. How can an electric force have an inverse-cube dependence? Doesn’t Coulomb’s law say that the electric force depends on the inverse square of the distance? Explain.

(a) Expression for the net force exerted on the dipole by the charge is

(b) Force toward .

Charged object exerts a net attractive force on an electric dipole, permanent electric dipole consisting of charges *+q* and* -q* separated by the fixed distance s. Charge *+Q* is the distance r from the center of the dipole and

The net force from the charge is coming from both the *+ve* and the* -ve* charges in the dipole. From the given figure, the distance from* q to Q* is, and so the force between these two charges is given by

here the force is negative because the two positive charges repel each other, it pushes the dipole away from it. Similarly, since the negative charge in the dipole is a distance away from* Q*, and is attractive, the force on *-q* is given by

Then the net force is *F*_{negative}*+F*_{positive}

Charged object exerts a net attractive force on an electric dipole, permanent electric dipole consisting of charges* +q* and -*q *separated by the fixed distance *s.* Charge *+Q *is the distance* r *from the center of the dipole and .

Because , the first term is bigger, and so the force is to the right and it's an attractive force.

Charged object exerts a net attractive force on an electric dipole, permanent electric dipole consisting of charges *+q* and *-q *separated by the fixed distance *s*. Charge *+Q *is the distance* r *from the center of the dipole and

Using a binomial expansion, , we can rewrite

And this force is attractive.

Charged object exerts a net attractive force on an electric dipole, permanent electric dipole consisting of charges *+q* and *-q *separated by the fixed distance *s*. Charge *+Q *is the distance* r* from the center of the dipole and

Coulomb's law applies between point charges. This situation is different- we have extended charge distributions. The negative charge is partially screened by the positive charge in the dipole. So, the force is not as strong. The force drops to zero because the dipole looks neutral at large distances; the two charges nearly cancel each other out.

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