An air-filled toroidal solenoid has a mean radius of 14.9 cmand a cross-sectiona

Question

An air-filled toroidal solenoid has a mean radius of 14.9 cmand a cross-sectional area of 4.98 cm2 as shown in (Figure 1). Picture this as the toroidal core around which the windings are wrapped to form the toroidal solenoid. The current flowing through it is 12.1 A , and it is desired that the energy stored within the solenoid be at least 0.385 J .

CH30 An Air-Filled Toroidal Solenoid Part A An air-filled toroidal solenoid has a mean radius of 14.9 cm and a cross-sectional area of 4.98 cm2 as shown in (Figure 1). Picture this as the toroidal core around which the windings are wrapped to form the toroidal solenoid. The current flowing through it is 12.1 A and it is desired that the energy stored within the solenoid be at least 0.385 J What is the least number of turns that the winding must have? Express your answer numerically, as a whole number, to three significant figures. View Available Hint(s) 8812 turns Submit Figure 1 of 1 Incorrect: Try Again: 4 attempts remaining average radius ra Provide Feedbaclk cross-sectional

Explanation / Answer

energy stored in the system

U = 0.5 L * i^2
  
L = (2U) / i^2

= 2*0.385/(12.1)^2

= 5.26*10^-3 H

Self inductance of the toroid is given by
L = ?oN2A/(2 ? R)

N = [ ( 2 ? R L)/ ( ?oA) ]^0.5

N = [ 2*3.14* 0.149* 5.26*10^-3/(4*3.14*10^-7* 4.98*10^-4)]^0.5

N= 2805 turns.

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comment in case any doubt..goodluck

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