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Q. 77

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

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 .

See the step by step solution

Step by Step Solution

Step 1: Given information (part a)

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

Step 2: Explanation (part a)

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 Fnegative+Fpositive

Step 3: Given information (part b)

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 .

Step 4: Explanation (part b)

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

Step 5: Given information (part c)

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

Step 6: Explanation (part c)

Using a binomial expansion, , we can rewrite

And this force is attractive.

Step 7: Given information (part d)

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

Step 8: Explanation (part d)

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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