How Fast Should the Smaller Solenoid Move to Induce 2.3V in the Larger Solenoid?

[aleksxxx]

Homework Statement

Assume the field inside the larger coil (.075m Radius, 1200 loops), reaches the maximum value when the smaller solenoid, (.05m radius, 1200 loops), is halfway inserted. with what constant velocity must the smaller solenoid be inserted to induce 2.3V in the larger solenoid?

Homework Equations

Eind=L(delta I/delta t)

L=[(mu0)(N^2)(A)]/l

The Attempt at a Solution

The problem does not give length of the solenoid, so I am pretty sure the second equation will not work. I can't find any other equations that would seem to help with this problem.

Am i missing something, or would i need more information to do the problem?
In part a we had to solve the length for solenoid "A" so that is would create a magnetic field of .0025T with a current of .13A - which i calculated to be 7.84cm --- but I am not sure if that is going to apply to this part of the problem.

Please point me in the right direction, if i have enough info just given in c, or if I am missing an equation.

thanks

 

[aleksxxx]

any ideas, anyone?

 

[m2003]

I would suggest that you use the equation for Faraday's law of induction, which states that the induced EMF (electromotive force) is equal to the rate of change of magnetic flux through a surface. In this case, the surface would be the cross-sectional area of the larger solenoid, and the magnetic flux would be the magnetic field created by the smaller solenoid as it is inserted into the larger one.

So, we can write the equation as:

Eind = -N * (delta B/delta t) * A

Where N is the number of loops in the larger solenoid, delta B/delta t is the rate of change of magnetic field (which is equal to the velocity of the smaller solenoid times the magnetic field created by the smaller solenoid), and A is the cross-sectional area of the larger solenoid.

We also know that the induced EMF is equal to 2.3V, and we can calculate the magnetic field created by the smaller solenoid using the equation for the magnetic field inside a solenoid:

B = (mu0 * N * I)/l

Where mu0 is the permeability of free space, N is the number of loops in the smaller solenoid, I is the current, and l is the length of the smaller solenoid (which we do not know, but can solve for later).

So, we can rewrite the equation for Eind as:

Eind = -N * (delta B/delta t) * A

= -N * (delta [(mu0 * N * I)/l]/delta t) * A

= -N * (mu0 * N * (delta I/delta t) * A)/l

= -[(mu0 * N^2 * A)/l] * (delta I/delta t)

We can substitute this into the equation for Faraday's law:

2.3V = -[(mu0 * N^2 * A)/l] * (delta I/delta t)

We know the values for mu0, N, A, and delta I/delta t, so we can solve for l:

l = [(mu0 * N^2 * A * delta I)/(2.3V * delta t)]

Now we can use this value of l to solve for the velocity of the smaller solenoid:

B = (mu0 *