Magnetic Circuits Questions and Answers

Answer: B

The field of a long straight current-carrying wire is \(B = \mu_0 I / (2\pi r)\). Substituting \(\mu_0 = 4\pi \times 10^{-7}\) T m/A, I = 5 A and r = 0.20 m gives:

This is 5 microtesla. The values 0.5, 50 and 500 microtesla are wrong by factors of 10, 10 and 100 and would result from slips in the power of ten or from using the wrong distance, for example 2 cm instead of 20 cm.

Answer: B

Cobalt is a ferromagnetic substance: like iron and nickel, it is strongly attracted by a magnet and can itself be magnetised, and it keeps its magnetism up to a high Curie temperature. Paramagnetic substances such as aluminium are only weakly attracted, diamagnetic substances such as copper are weakly repelled, and a non-magnetic substance is not affected. The answer is ferromagnetic substance, option (B). Iron, cobalt and nickel are the three common ferromagnetic metals, and their strong attraction is due to the alignment of groups of atoms called domains.

Answer: B

Mu-metal is a nickel-iron alloy of very high magnetic permeability, so it conducts magnetic flux well and screens against stray magnetic fields. The key gives instrument transformers as the application, since the high permeability and low losses suit their cores, and the metal is also used as a magnetic shield. It is not used for induction type relays, for the field and armature of DC machines, which use steel and silicon steel, or for the star-delta starter. The answer is Instrument transformers, option (B).

Answer: D

The statement that is not a property of a magnet is that the pole strength of the north pole is always higher than that of the south pole. The two poles of a magnet have equal strength and opposite polarity, which is why isolated poles do not exist.

The other statements are true: like poles repel each other, unlike poles attract each other, and every magnet has two poles. The fourth option is the answer.

Answer: C

The mutual inductance between two coils placed close together is inversely proportional to the length of the coil. For two coils on the same core:

\[ M = \frac{\mu_0 \mu_r N_1 N_2 A}{l} \]

M increases with the number of turns, the permeability and the cross-sectional area, and falls as the length l of the coil increases. The first, second and fourth options are factors that increase M, so the third option is the answer.

Answer: B

The total inductance of the parallel combination is 1 mH. Inductors in parallel combine like resistors in parallel, when there is no mutual coupling.

\[ \frac{1}{L} = \frac{1}{10} + \frac{1}{5} \]

\[ + \frac{1}{5} + \frac{1}{2} = 1\ \text{mH}^{-1} \]

So L = 1 mH. The value 22 mH is the sum of the four inductances, which is the series value, and 10 mH and 7 mH are not the result of the parallel formula. The second option is correct.

Answer: A

The coefficient of coupling is 0.5. It is the ratio of the mutual inductance to the geometric mean of the two self inductances.

\[ k = \frac{M}{\sqrt{L_1 L_2}} \]

\[ = \frac{30}{\sqrt{40 \times 90}} = \frac{30}{60} = 0.5 \]

The values 0.6, 0.7 and 0.8 do not equal 30 divided by 60. The fact that the coils are connected in series does not change the formula for k. So the first option is correct.