If you were to cut a small permanent bar magnet in half, a) none of these statements is true. b) one piece would be a magnetic north pole and the other piece would be a south pole. c) each piece would in itself be a smaller bar magnet with both north and south poles. d) neither piece would be magnetic.

Explanation:

According to classical physics, a magnetic field always has two associated magnetic poles (north and south), the same happens with magnets. This means that if we break a magnet in half, we will have two magnets, where each new magnet will have a new south pole, and a new north pole. However, the magnetic force of each magnet will be less than that of the original magnet.

This is because for classical physics, naturally, magnetic monopoles can not exist.

Nevertheless,  according to quantum physics, magnetic monopoles do exist, which was predicted by Paul Dirac in 1981. This has led to several experiments and investigations, among which the most recent one so far (year 2014), is the experiment led by a group of scientists from the Amherst College (United States) and the University of Aalto (Finland), that reported having synthesized for the first time in a laboratory a magnet of a single magnetic pole.

most voltage drop calculators want the distance between the source and destination. then internally, they double it so both the source and return wires are calculated. but you need to know which distance the calculator uses so you're not half of what you should be or double what you should be.

most circuit breakers will not take a #6 directly, so the electrician will have to splice on a smaller pigtail. you also have to upsize the grounding wire when you upsized the ungrounded (hot) wire (see note in 250.122). this will preclude using most cable assemblies, as a cable with #6 copper will most likely only have a #10 grounding conductor. you need a #6 grounding conductor if the circuit is 20a. a #8 cable is no better, as it will have a #10 grounding conductor too. but most 20a breakers will take a #8 directly.

in your related post, you didn't say what type of load this is. if it is a light or heater, voltage drop won't be a big issue. if this is a motor, the current needs are huge at startup and the voltage drop can pose a problem. if this is a motor, knowing if the motor is under much load during startup will answer the voltage drop effect (a saw is easier to start than a compressor).

the answer is the first electromagnet (a). this is because it has more coils around the ferromagnetic material. increasing the number of coils increases the surface area in which the metal interacts with the current in the coil. this enables more atoms in the metal to become aligned hence becoming more magnetized.