Physics Demystified, 2nd edition
Stan Gibilisco
Explanations for Quiz Answers in Chapter 9
1. We can calculate magnetomotive force in ampere-turns (At) for any DC-carrying wire coil by calculating the product of the number of turns and the current in amperes. In this case, we have a 100-turn coil carrying 200 mA (0.200 A) of DC. The magnetomotive force is therefore 100 x 0.200 = 20.0 At. The correct choice is C.
2. If we connect an electromagnet to a source of sine-wave AC, the resulting magnetic field will reverse its polarity twice for each AC cycle. The instantaneous field intensity will vary along with the instantaneous current in the electromagnet's coil. The correct choice is A.
3. By definition, a diamagnetic material has a permeability factor of less than 1, indicating that it "spreads out" (or dilates) magnetic lines of flux compared with the same amount of magnetomotive force in a vacuum. The answer is D.
4. In the vicinity of a straight span of wire carrying constant DC, the magnetic lines of flux are actually circles that all lie in planes perpendicular to the wire, and whose centers all coincide with the wire axis. The correct choice is C.
5. The ideal core material for making an AC electromagnet will have high permeability, so that it concentrates the magnetic lines of flux to a large extent. The ideal core material will also exhibit low retentivity, so that it can follow along easily with rapid changes in the instantaneous magnetic flux density. The correct choice is B.
6. This question is a little bit tricky, so we have to pay close attention to its wording! We have a coil that carries a large DC, but we aren't told, and we don't know, the exact amount of current. We find a rod made of a certain ferromagnetic material. The rod's manufacturer tells us that the magnetic flux density inside the material can reach, but never exceed, 800 G. The core material has a so-called saturation flux density of 800 G. We insert the rod in the coil and observe 800 G of flux density inside the rod, so we know that it's saturated. Then we remove the rod from inside the coil. We observe a flux density of 20 G inside the rod. We can calculate the rod's retentivity as 20/800 = 0.025 = 2.5%, but we can't calculate its permeability. We must therefore choose A as the answer.

7. To solve this problem, we must use the formula for magnetic flux density Bt (in teslas) for a coil having n turns, carrying a current I (in amperes), surrounding a core with permeability µ, and having an end-to-end length of s (in meters). That formula, which appears on page 276 of the text, is

Bt = 1.2566 x 10-6 µnI / s

We've been assured that the core material has not reached a state of saturation, so we know that we can use the above formula and expect valid results. We're given the following input parameters:

s = 10 cm = 0.10 m
n = 400
µ = 1.5 x 105
Bt = 0.30 T

Plugging these values into our formula, we get

0.30 = 1.2566 x 10-6 x 1.5 x 105 x 400 x I / 0.10
= 753.96 I

which solves to I = 0.00040 A = 0.40 mA. The correct choice is A.
8. We can express the overall quantity of a magnetic field in either webers or maxwells. The correct choice is B. Remember, overall magnetic-field quantity is not the same thing as magnetic flux density, which we express in teslas or gauss.

9. Let's use the formula for magnetic flux density Bt (in teslas) at a specific distance r (in meters) from a straight wire carrying a current I (in amperes). That formula, which appears on page 268, is

Bt = 2 x 10-7 I / r

We're told that r = 2.50 m and I = 500 mA = 0.500 A. We can express the coefficient of 2 in the foregoing equation to as many significant figures as we need, because that coefficient is mathematically exact. Therefore

Bt = 2.00 x 10-7 x 0.500 / 2.50
= 4.00 x 10-8 T
= 4.00 x 10-4 G

The correct choice is D.
10. The only parameter that we change in this situation is the number of coil turns, which we increase from 100 to 400, a factor of exactly 4. Let's look at the formula for flux density that we used to calculate the answer to Question 7. This formula tells us that the flux density inside the coil varies in direct proportion to the number of coil turns. If we increase that number by a factor of 4 but don't change any other parameter in the equation, we'll increase the flux density inside the coil (and also inside the core material) by a factor of 4. The correct choice is B.