Question

a thin 12 - cm - long solenoid has a total of 470 turns of wire and carries a current of 1.8 a. part a calculate the field inside the solenoid near the center. express your answer using two significant figures. b = t

Explanation:

Step1: Convert the length unit

Convert the length of the solenoid from centimeters to meters.
$$l = 12\ cm=0.12\ m$$

Step2: Calculate the number of turns per unit length

The number of turns per unit length \(n=\frac{N}{l}\), where \(N = 470\) turns and \(l = 0.12\ m\).
$$n=\frac{470}{0.12}\ m^{-1}\approx3916.67\ m^{-1}$$

Step3: Use the formula for the magnetic field inside a solenoid

The formula for the magnetic field inside a solenoid is \(B=\mu_0nI\), where \(\mu_0 = 4\pi\times10^{-7}\ T\cdot m/A\) and \(I = 1.8\ A\).
$$B=(4\pi\times 10^{-7})\times\frac{470}{0.12}\times1.8$$
$$B=(4\pi\times10^{-7})\times3916.67\times1.8$$
$$B\approx9.0\times10^{-3}\ T$$

Answer:

\(B = 9.0\times10^{-3}\ T\)