It is desired to construct a solenoid that will have a resis

It is desired to construct a solenoid that will have a resistance of 4.90 Ohm (at 20.0 degree C) and produce a magnetic field of 4.70 Times 10^-2 T at its center when it carries a current of 3.80 A. The solenoid is to be constructed from copper wire having a diameter of 0.500 mm. If the radius of the solenoid is to be 1.00 cm, determine the number of turns of wire needed. Turns If the radius of the solenoid is to be 1.00 cm, determine the required length of the solenoid. cm

Solution

(A) for r = 1cm = 0.01 m

field due to solenoid at centre, B = u0 N I / 2 R

4.70 x 10^-2 = (4pi x 10^-7)(N) (3.80) / (2 x 0.01)

N = 197 turns

(B)    B = u0 (N/L) I

4.70 x 10^-2 = (4pi x 10^-7) (197/ L) (3.80)

   L = 0.02 m or 2 cm