1. A long, current-carrying solenoid with an air core has 1650 turns per meter o

Question

1. A long, current-carrying solenoid with an air core has 1650 turns per meter of length and a radius of 0.0220 m. A coil of 100 turns is wrapped tightly around the outside of the solenoid, so it has virtually the same radius as the solenoid. What is the mutual inductance of this system?

2. A generator uses a coil that has 360 turns and a 0.53-T magnetic field. The frequency of this generator is 60.0 Hz, and its emf has an rms value of 120 V. Assuming that each turn of the coil is a square (an approximation), determine the length of the wire from which the coil is made.

Explanation / Answer

Solution:

Q.1) Using the formula

=> M ( mutual inductance) = 0 N1 N2 A

=> M = 4 x 3.14 x 10^-7 x 1650 x 100 x 3.14 x (0.0220)^2

=> M = 39.4384 x 165 x 10^-4 x (0.022)^2

=> M = 3.15 x 10^-4 H

Q.2) Given rms voltage = 120 V

Now V0 ( peak voltage ) = 120 x 1.414

=> V0 = 169.68 V

Using the formula e = B x A x w x n ( w is angular frequency )

=> A = e / B x w x n

=> A = 169.68 / ( 0.53 x 2 x 3.14 x 60 x 360)

=> A = 0.00236 m^2

So side of the coil = sqrt ( 0.00236)

=> side = 0.04987

length of the coil wire = 4 x 0.04987 x 360

length = 69.95 m (approximately)

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