A solenoid that has length 30 cm, radius 1.2 cm, and 315 turns carries a current

Question

A solenoid that has length 30 cm, radius 1.2 cm, and 315 turns carries a current of 2.9 A. Find the magnitude of the magnetic field on the axis of the solenoid at the following locations:

(a) at the center of the solenoid
                 mT

(b) at one end of the solenoid
                mT

A circuit consists of a resistor, an ideal 1.6-H inductor and an ideal 60-Hz generator, all connected in series. The rms voltage across the resistor is 28 V and the rms voltage across the inductor is 34 V.

(a) What is the resistance of the resistor?
                      k

(b) What is the peak emf of the generator?
                      V

Explanation / Answer

magnetic field at the center = k * number of turns * current / sqrt(length^2 + radius^2)

magnetic field at the center = 2 * pi * 10^-7 * 315 * 2.9 / sqrt(0.3^2 + 0.012^2)

magnetic field at center = 0.00191 T

magnetic field at ends = k * number of turns * current / sqrt((length / 2)^2 + radius^2)

magnetic field at ends = 2 * pi * 10^-7 * 315 * 2.9 / sqrt(0.15^2 + 0.012^2)

magnetic field at ends = 0.003814 T

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