A solenoid 1000 cm in diameter and 650 cm long is made from

A solenoid 10.00 cm in diameter and 65.0 cm long is made from copper wire of diameter 0.100 cm, with very thin insulation. The wire is wound onto a cardboard tube in a single layer, with adjacent turns touching each other. What power must be delivered to the solenoid if it is to produce a field of 6.00 mT at its center?

Solution

the number of turns is calculated as follows:

   N = 65/0.1 = 650

Magnetic field is,

   B = Nu_oI/L

Current is,

   I = B L / Nu_o = 6x10^-3 * 0.65 / 650*4*pi*10^-7 = 4.777 A

Resistance is,

      R = pL_wire/A = 1.7X10^-8 * [2*pi*0.05*650] / pi*[0.1x10^-2/2]^2 =4.42 ohms

the power is,

   P = I^2R = 4.777*4.777*4.42 = 100.86 W