How to solve these two questions?

1) See attached figure

The relationship between charge and current is:

where

i is the current

Q is the charge

t is the time

Therefore, the current is the rate of change of the charge passing through a given point over time.

This means that for a graph of charge over time, the current is just equal to the slope of the graph.

For the graph in this problem:

- Between t = 0 and t = 2 s, the slope is

therefore the current is

i = 25 A

- Between t = 2 s and t = 6 s, the slope is

therefore the current is

i = -25 A

- Between t = 6 s and t = 8 s, the slope is

therefore the current is

i = 25 A

The figure attached show these values plotted on a graph.

2)

The previous equation can be rewritten as

This equation is valid if the current is constant: if the current is not constant, then the total charge is simply equal to the area under a current vs time graph.

Here we have the current vs time graph, so we gave to find the area under it.

The area of the first triangle is:

While the area of the second square is

So, the total area (and the total charge) is

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.