An ideal solenoid of length $10 \mathrm {~cm}$ consists of a wire wrapped tightly around a wooden core. The magnetic field strength is $4.0 \mathrm {~T}$ inside the solenoid. If the solenoid is stretched to $25 \mathrm {~cm}$ by applying a force to it, what does the magnetic field become?
A) $20 \mathrm {~T}$
B) $4.0 \mathrm {~T}$
C) $10.0 \mathrm {~T}$
D) $1.6 \mathrm {~T}$

Question

Quizplus · Accepted Answer

The magnetic field inside an ideal solenoid is given by $B = \mu_0 n I$, where $n$ is the number of turns per unit length, $I$ is the current, and $\mu_0$ is the magnetic constant. Stretching the solenoid increases its length but does not change the total number of turns or the current. Therefore, the number of turns per unit length decreases, which decreases the magnetic field strength. Since the length increases from $10 \mathrm{~cm}$ to $25 \mathrm{~cm}$, or by a factor of $2.5$, the magnetic field strength decreases by the same factor, from $4.0 \mathrm{~T}$ to $1.6 \mathrm{~T}$.

An Ideal Solenoid of Length 10 cm10 \mathrm {~cm}10 cm Consists of a Wire Wrapped Tightly Around a Wooden Core

An Ideal Solenoid of Length $10 \mathrm {~cm}$ Consists of a Wire Wrapped Tightly Around a Wooden Core