A solenoid 4.0 cm in radius and 4.0 m in length has 8 000 uniformly spaced turns and carries a current of 5.0 A. Consider a plane circular surface (radius = 2.0 cm) located at the center of the solenoid with its axis coincident with the axis of the solenoid. What is the magnetic flux through this surface? (1 Wb = 1 T ⋅ m²) A) 63 μWb B) 16 μWb C) 0.25 mWb D) 10 μWb E) 5.0 μWb

Question

Quizplus · Accepted Answer

The magnetic field inside a solenoid is given by $B=\mu_0 ni$, where $\mu_0$ is the magnetic constant, $n$ is the number of turns per unit length, and $i$ is the current. In this case, $n=\frac{8000	ext{ turns}}{4	ext{ m}}=2000	ext{ turns/m}$, so $B=\mu_0(2000~	ext{turns/m})(5.0~	ext{A})=\mu_0(10,000~	ext{A/m})$.

The magnetic flux through the circular surface can be found using $\Phi_B=B\cdot \pi r^2$, where $r$ is the radius of the circular surface. Plugging in the values, we get $\Phi_B=\mu_0\pi(10,000 ~	ext{A/m})(0.02~	ext{m})^2=16	imes 10^{-6}~	ext{Wb}$.

Thus the answer is B) 16 μWb.

A Solenoid 4