A solenoid of radius $1.1 \mathrm{~cm}$, carrying a current of $2.2 \mathrm{~A}$, produces a magnetic field at its center of $0.28 \mathrm{~T}$. How many turns per unit length does the solenoid have?
A) $1.0 \times 10^{5} \mathrm{~m}^{-1}$
B) $1.1 \times 10^{3} \mathrm{~m}^{-1}$
C) $7.0 \times 10^{3} \mathrm{~m}^{-1}$
D) $1.0 \times 10^{-9} \mathrm{~m}^{-1}$
E) $2.2 \times 10^{3} \mathrm{~m}^{-1}$

Question

Quizplus · Accepted Answer

The magnetic field at the center of a solenoid is given by:$$B = \mu_0 n I$$where:* $B$ is the magnetic field* $\mu_0$ is the permeability of free space* $n$ is the number of turns per unit length* $I$ is the currentSolving for $n$, we get:$$n = \frac{B}{\mu_0 I}$$Plugging in the given values, we get:$$n = \frac{0.28 \mathrm{~T}}{4\pi \times 10^{-7} \mathrm{~T \cdot m/A} \times 2.2 \mathrm{~A}} = 1.0 \times 10^{5} \mathrm{~m}^{-1}$$Therefore, the correct answer is A.

A Solenoid of Radius 1.1 cm1.1 \mathrm{~cm}1.1 cm , Carrying a Current Of 2.2 A2.2 \mathrm{~A}2.2 A

A Solenoid of Radius $1.1 \mathrm{~cm}$ , Carrying a Current Of $2.2 \mathrm{~A}$