An ideal solenoid having a coil density of 5000 turns per meter is 10 cm long and carries a current of 4.0

a. what is the strength of the magnetic field at its center?

The rule that is used to get the strength of magnetic field at the center of solenoid (B) is:

B = µ x n x I where:

µ is the permeability of the medium where the solenoid is based. In this problem, the medium is air which means that µ = µ o = 4 pi x 10^-7 Tm/A

I is the current passing (I = 4 amperes)

n is the number of turns per unit length (5000 turns)

Substituting in the mentioned equation, we find that:

B = 4 x 3.14 x 10^-7 x 5000 x 4 = 25.132 mT