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Chapter 4: Q17E (page 1014)

An air-filled toroidal solenoid has a mean radius of15cmand a cross-sectional area of5cm2. When the current is12A, the energy stored is0.39J. How many turns does the winding have?

Short Answer

Expert verified

The number of turns is2580.

Step by step solution

01

The formulas used in the problem

The stored energy in the toroid solenoid is given byU=12LI2.

The self-inductance in a toroid is given byL=渭0N2A2蟺r.

02

Use the two equations to find the number of turns

Given thatr=15cm,A=5cm2,U=0.39JandI=12A.

Using the two equations, the number of turns can be given by

N=2蟺rL渭0AN=2蟺脳0.15脳5.417脳10-34蟺脳10-7脳5脳10-4N=2580

So, the number of turns is2580.

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