Question

A toroidal solenoid has an inner radius of 12.0 cm and an outer radius of 15.0 cm . It carries a current of 1.50 A . Part A How many equally spaced turns must it have so that it will produce a magnetic field of 3.75 mT at points within the coils 14.0 cm from its center? Enter your answer numerically. mastering physics

Answer 1

The number of turns is
`N  = 1750 \ turns`

Step-by-step explanation:

From the question we are told that

The inner radius is
`r_i =  12.0 \  cm  =  0.12 \  m`

The outer radius is
`r_o =  15.0 \  cm  =  0.15 \  m`

The current it carries is
`I =  1.50 \  A`

The magnetic field is
`B  =   3.75 mT = 3.75 *10^(-3) \  T`

The distance from the center is
`d =  14.0 \ cm  =  0.14 \  m`

Generally the number of turns is mathematically represented as

`N  =  (2 *  \pi  * d  *  B)/( \mu_o *  r_o )`

Generally
`\mu_o` is the permeability of free space with value

`\mu_o  =  4\pi * 10^(-7) \ N/A^2`

So

`N  =  (2 *  3.142   * 0.14 *  3.75 *10^(-3) )/( 4\pi * 10^(-7)  * 0.15  )`

`N  = 1750 \ turns`