One coil carrying a current can induce a current in a nearby coil of wire. That\

Question

One coil carrying a current can induce a current in a nearby coil of wire. That's called "Mutual Inductance". But the one coil can create an effect in itself, called "Self-Inductance."

A solenoid has a length L. Radius R, has N turns and carries a current I. Use values of L, N, R and I provided in lab to calculate the inductance: N = 2490, I=6A, L=.14m, R=1.6m

What is the magnetic field produced by this solenoid at its center, along the axis Show which formula you are using and give a numerical answer.

What is the flux of magnetic field through one turn of the solenoid?Show which formula you are using and give a numerical answer.

That flux passes through each turn of wire in the solenoid. That quantity is called the Flux Linkage. What is the Flux Linkage for this solenoid?Show which formula you are using and give a numerical answer.

What is the value for the inductance of this solenoid? Show which formula you are using and give a numerical result.

You began using the value of current passing through the solenoid. Docs the inductance depend on the amount of current?

If you were to do a similar calculation for the capacitance of a pair of parallel plates, would the capacitance depend on the amount of charge on the plates or on the voltage the plates were held at? Explain why it does or why it does not.

Explanation / Answer

Given, length of solenoid = L

Radius of solenoid = R

numbr of turns = N

current = I

a. let inductance of a solenoid be l

then l = mu*N^2*A/L [ formula for self inductance of a solenoid]

but A = pi*R^2

so, l = mu*N^2*pi*R^2/L

now plugging in values from the question

l = 4*pi*10^-7 *2490^2 * pi*1.6^2/0.14 = 447.579 H

b. magnetic field on the axis of a long solenoid, B = mu*N*I/L

plugging in vaslues form the question

B = 4*pi*10^-7 *2490 * 6/0.14 = 0.134 T

c. flux of magnetic field thourgh one turn of the coil = B*A = B*pi*R^2 = 0.134*pi*(1.6^2) = 1.07769 Wb

d. Flux linkage = flux through all the loops = NBA = muN^2I*A/L = 2683.4529 Wb

e. indictance, L = flux linkage per unit current = NBA/I = mu*N^2*piR^2/L = 447.579 H

f. the inductance does not depends on the current in the solenoid and just depends on the physical properties on it

g. No, as itr is a physical property of the capacitor and does not depend on charge or voltage between the capacitor plates

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