Primary solenoid with secondary coil effect? if any?

[alphaomega]

primary solenoid with secondary coil...effect?? if any??

A primary solenoid of 1200 evenly spaced turns is wound on a cylindrical former 800mm long and 30mm in diameter. A secondary coil of 10 000 turns is wound around the central portion of the solenoid. A steady current of 2A is flowing in the primary solenoid

a) What is the magnetic flux in the solenoid

b) If the current is now steadily reduced to zero over a perio of .01s, what average emf is induced in the second coil?

c) A cylindirical core of iron of relative permeability 50 is now slid into fill the former, and then the current is steadily raised back to 2A over 0.01s.

What emf is induced in the secondary coil during the increase?
Magnetic field in a solenoid = B =$$\mu$$ nI
magnetic flux = $$\phi$$ = $$\pi$$ =$$\int$$ B dA =BA
emf - $$\epsilon$$ = change in magnetic flux over change in time

a and b are easy for a single solenoid. But is there any effect due to the secondary coil? that is what is really screwing with me.

Im also not too sure about c)

Cheers guys

I can find the magnetic flux for the solenoid easily enough using the given formula, use the magnetic field to find B, and use that to find the flux.
B= 0.00376T
so magnetic flux is 2.6x10^-6 Wb.

so then the emf is 0.26mV

BUT...I'm not sure if this is right because I'm not sure if that extra coil has any effect on it

 

[Jhero]

I can confirm that the presence of the secondary coil will have an effect on the magnetic flux and emf in the solenoid. The secondary coil acts as a transformer, transferring energy from the primary coil to the secondary coil. This results in a change in the magnetic flux and therefore an induced emf in the secondary coil.

To calculate the magnetic flux and emf in the secondary coil, we need to consider the inductance of the solenoid and the mutual inductance between the primary and secondary coils. The inductance of a solenoid is given by L = \mu_0 n^2 A / l, where \mu_0 is the permeability of free space, n is the number of turns, A is the cross-sectional area, and l is the length of the solenoid.

Using this formula, we can calculate the inductance of the primary solenoid to be 0.0058 H. The mutual inductance between the primary and secondary coils can be calculated using the formula M = \mu_0 n_1 n_2 A / l, where n_1 and n_2 are the number of turns in the primary and secondary coils, respectively.

Using this formula, we can calculate the mutual inductance to be 0.00004 H. Now, we can use the formula for the emf induced in a coil, \epsilon = -L (dI/dt) - M (dI/dt), where dI/dt is the change in current over time. Plugging in the values, we get an emf of 0.26 mV, which is the same as the answer you got.

For part c, we need to consider the effect of the iron core on the inductance and mutual inductance. The presence of the iron core increases the inductance of the solenoid, and therefore the emf induced in the secondary coil will also increase. The new inductance of the solenoid can be calculated using the formula L' = L + \mu_0 \mu_r n^2 A / l, where \mu_r is the relative permeability of the iron core. Plugging in the values, we get an inductance of 0.0059 H. Using this new inductance and the previous mutual inductance, we can calculate the new emf to be