Question

One solenoid is centered inside another. The outer one has a length of 45.0 cmcm and contains 6750 coils, while the coaxial inner solenoid is 5.00 cmcm long and 0.150 cmcm in diameter and contains 17.0 coils. The current in the outer solenoid is changing at 35.5 A/sA/s .

A) What is the mutual inductance of these solenoids?

Express your answer in microhenrys.

B) Find the emf induced in the inner solenoid.

Express your answer in volts.

Answer 1

A) Here we have given that the 2 concentric solenoids in which a the rate of change of current occurs in outer solenoid at 35.5A/s.Due to the change of flux of the inner coil(2) by the change of current in outer coil(1) with time an emf is induced in the outer coil by the occurance of mutual induction in the concentric coil system.

here we have given the datas,

length of outer coil, l1=45cm

number of turns of outer coil, N1=6750coils

length of inner coil, l2=5cm

diameter of inner coil=0.15cm

radius og inner coil,r=0.15/2=.075cm

number of turns in inner coil, N2=17coils

rate of change of current in outer coil,

from the expression derived for mutual induction for the system,ie,

(magnetic permmeaility of vaccum)

here,for mutual induction lower area(area of inner coil)and larger length(45cm) should be taken,

area of inner coil,

substituting the given values in equation,

M=(4x3.14x10^(-7)x6750x17x1.7662x10^(-6))/(45x10^-2)

M=5.6596x10^-7 Henry

B)induced emf in the inner coil by mutual induction is the rate of change of flux of the coil by the rate of change of current in the outer coil.

we have,flux generated in the inner coil,

I=current passing through the inner coil.

so,emf induced,

induced emf in the inner coil,