Difficult Physics question (6 marks)

A student is to investigate the magnetic field inside and around a solenoid.
It is suggested that the magnetic field strength B inside a long solenoid is determined by
various quantities, namely B ∝ NI/L
where N is the number of turns, L is the length of the solenoid and I is the current in the
wire.
Apparatus is set up for an experiment as shown in Figure 6.1.
Fig. 6.1 (Slinky connected to signal generator and oscilloscope)
A Slinky is a long spring about 70 mm in diameter which can be stretched easily and
uniformly. The search coil has 5000 turns and the signal generator can produce a
constant alternating current at a frequency between 0 and 1 kHz.
Plan an experiment using this equipment to investigate the validity of the relationship
between B, at the centre of the solenoid, and one of the variables N or L. Explain how
you will make your measurements, how sensitive they will be and the steps that you will
take to make this a valid test.
plan P
• investigate one variable with the other fixed
• oscilloscope time base can be off
• do rough preliminary test over range of variable to check that
there is a suitable variation in oscilloscope V
• choose and fix f of I and value of other variable (M3);
• measure e.m.f. V for 5 or 6 settings of variable from oscilloscope
screen
sensitivity S
• magnitude of detected signal depends on rate of change of flux
linkage/Faraday's law through search coil
• so increases with f and B (N and A of search coil are fixed)
• for large B use small L f changing N
or large N if changing L
Could someone explain the plan to me, and why rate of change of flux increases with f and B?

All flux is is the strength of the magnetic field per unit area (i.e. a density of field strength), and the rate at which you sweep it out is the rate of change of flux. So if you're moving faster (or have a higher frequency) you're sweeping out more flux per second, and if there is more to begin with (or have more magnetic field strength) then you're also sweeping out more flux per second.
Not to be annoying but I haven't read the stuff about the experiment; I usually just learn the markscheme for those kinds of things. The theory above should probably give you the inspiration to answer this though.

Thanks but one more thing, when they mention investigate one variable with other fixed in MS would you only write that in the exam and also is a 'preliminary' test a commonality with oscilloscopes to include with every question?