A 1000-turn solenoid is 50 cm long and has a radius of 2.0 cm.It carries a current of 8.0 A.What is the magnetic field inside the solenoid near its center? A)2.0 $\times$ 10^-2 T B)3.2 $\times$ 10^-3 T C)4.0 $\times$ 10^-4 T D)1.0 T E)2.0 $\times$ 10^-4 T

Question

Quizplus · Accepted Answer

We know that the magnetic field of a solenoid is given by:

B = μ₀nI

where μ₀ is the permeability of free space, n is the number of turns per unit length, and I is the current.

We can find n by dividing the total number of turns (1000) by the length of the solenoid (50 cm):

n = N/L = 1000/0.50 = 2000 turns/m

Substituting in the values, we get:

B = μ₀nI = (4π×10⁻⁷ T·m/A)(2000 turns/m)(8.0 A) = 2.0×10⁻² T

Therefore, the magnetic field inside the solenoid near its center is 2.0×10⁻² T, which is equivalent to choice A.

A 1000-Turn Solenoid Is 50 Cm Long and Has a Radius