Mutual Inductance for a Pair of Coils

[mjk71]

Homework Statement

[URL]http://nplq1.phyast.pitt.edu/res/csm/csmphyslib/type66_inductance/PairOfCoils.jpg[/URL]
Coil A is a large 400 turn circular coil of radius 91.0 cm. Circular coil B has 160 turns, a radius of 2.0 cm and is located L = 92.0 cm from coil A along the same axis. The planes of the two coils are parallel. 1.) Find approximately the mutual inductance of this pair of coils. 2.) If the current in coil A varies with time according to I = 14t³ - 59t² - 1, where I is in amps and t is in s, find the magnitude of the EMF induced in coil B at time t = 1.0 s.

N₁ = 400 turns
N₂ = 160 turns
R₁ = .02 m
R₂ = .91 m
L = .92 m
t = 1.0 s
I(t) = 14t³ - 59t² - 1

Homework Equations

$$\epsilon$$_L = N₁N₂$$\Pi$$R²₂/2R₁ * di(t)/dt

The Attempt at a Solution

I attempted to solve for mutual inductance by: N₁N₂*pi*R²₂/2R₁
And then multiplied by the derivative of I(t) at t=1.0s for the induced emf, but I'm not getting the correct answer. Any help or direction would be appreciated.

 

[cupid.callin]

Hi mjk71

Welcome to PF !

Was the mutual inductance you got correct?

 

[mjk71]

Unfortunately, no.

 

[cupid.callin]

Its really late here ... I'll answer your question in morning ..:zzz:

 

[cupid.callin]

Hi mjk71

The situation is somethinglike this

let there be a current i in bigger loop. find the field on axis of bigger loop at the distance where smaller loop is placed

find flux and then divide it by i
you'll get inductance M