An experiment is being devised for students to undertake, that specifically includes a task to create an electromagnet by winding conducting wire around a cylindrical object and connecting it to a DC circuit using a battery. The experiment needs a length of wire to create a coil where the diameter of the resultant coil is $1\mathrm{.}0$ cm with a total of $100$ turns. This coil is then placed in the centre of a solenoid constructed with $400$ turns and a diameter of $2\mathrm{.}5$ cm with the current supplied from a battery of $15$ A$.$ Answer the following questions: a$)[$out of $1$ mark$]$ What is the magnetic field that the coil is exposed to$?$ b$)[$out of $2$ marks$]$ What is the magnetic flux through the centre of the solenoid? Assume for this scenario the current is steady. c$)[$out of $2$ marks$]$ If the current in the solenoid drops steadily to zero, what is the magnitude of the emf that is induced in the coil? Assume for this question the current takes $30$ ms drops to $0$ A$.$