Self inductance of a solonoidal coil

[samblue]

Homework Statement

A long, solonoidal coil with 2000 turns produces a B field pf 3mT at its center when a current of 1A flows through the coil. If the cross sectional area of the coil is: 2*10^-3 m^-2, and the field is uniform throghout the solonoid, determine the self inductance of the oil.

A small coil, C, is now plaed in the middle of the solonoid as such that the axis of the coils concide. The coil C has 10 turns, and a cross setional area of 4*10^-5m^2. Calculate the mutual inuctance between C and the solenoid.

Homework Equations

emf=-Nd(flux demnsity)/dt

L=flux density/current

The Attempt at a Solution

Dont really have many ideas about this question. I cannot work out how I am going to be able to use the data given as I do not know the emf?
thanks

 

[samblue]

On a second though to I have to use the formula:

B=U0*NI/L

If I do why am I given the area?

 

[Moetasim]

I would recommend approaching this problem by first understanding the concepts of self inductance and mutual inductance. Self inductance is a property of a circuit element that causes it to resist changes in current flow, while mutual inductance is a measure of the interaction between two circuits that causes a change in the magnetic field of one circuit to induce an emf in the other circuit.

To solve for the self inductance of the solenoid, we can use the equation L = B/I, where B is the magnetic field and I is the current. We are given values for both of these, so we can calculate the self inductance.

To determine the mutual inductance between the solenoid and the small coil, we can use the equation M = N1N2Φ/I1, where N1 and N2 are the number of turns in each coil, Φ is the magnetic flux, and I1 is the current in the first coil (in this case, the solenoid). Again, we are given values for all of these variables, so we can calculate the mutual inductance.

Additionally, we can use the given equation for emf to help us solve for the mutual inductance. Since we know the current and the flux density, we can rearrange the equation to solve for the mutual inductance.

It is important to also consider the units of the given values and make sure they are consistent with the units in the equations. If they are not, unit conversions may be necessary.

In summary, to solve this problem, we need to use the equations for self inductance and mutual inductance, along with the given values, to calculate the desired quantities. It is also helpful to have a good understanding of the concepts behind these equations.