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Two toroidal solenoids are wound around the same form so that the magnetic field of one passes through the turns of the other. Solenoid 1 has 700 turns, and solenoid 2 has 400 turns. When the current in solenoid 1 is 6.52 A, the average flux through each turn of solenoid 2 is 0.0320 Wb. (a) What is the mutual inductance of the pair of solenoids? (b) When the current in solenoid 2 is 2.54 A, what is the average flux through each turn of solenoid 1?

Short Answer

Expert verified

(a)The mutual inductance of the pair of solenoids is1.96H

(b) When the current in solenoid 2 is 2.54 A, the average flux through each turn of solenoid 1 is

Step by step solution

01

Definition of magnetic flux and mutual inductance

Magnetic flux is defined as the number of magnetic field lines passing through a given closed surface. It provides the measurement of the total magnetic field that passes through a given surface area.

Mutual inductance is a measure of the mutual inductionbetween two magnetically linked circuits, given as the ratio of the induced emf to the rate of change of current producing it.

It is expressed as,

M=ϕB2I1N2

Where ϕB2is magnetic flux linked with second coil having turns N2when current I2is flowing in first coil.

02

Calculate magnetic flux and mutual inductance

Two toroidal solenoids are wound around the same form so that the magnetic field of one passes through the turns of the other. Solenoid 1 has N1=700turns, and solenoid 2 has N2=400turns. When the current in solenoid 1 is I1=6.52A, the average flux through each turn of solenoid 2 is ϕB2=0.0320Wb.

(a)The mutual inductance of the pair of solenoids is calculated as,

role="math" localid="1664167297382" M=N2ϕB2I1

role="math" localid="1664167303363" M=400x0.03206.52M=1.96H

(b) When the current in solenoid 2 is I2=2.54A, the average flux through each turn of solenoid 1 is,

role="math" localid="1664167581172" ϕB1=MI2N1ϕB1=1.96×2.54700ϕB1=7.11×10-3Wb

Therefore,

(a) The mutual inductance of the pair of solenoids is 1.96H;

(b) When the current in solenoid 2 is 2.54 A, the average flux through each turn of solenoid 1 is 7.11×10-3Wb.

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