Question

A magnetic field of 0.90 T is aligned vertically with a flat plane. The magnetic flux through the plane is 7.3 × 10^-3 Wb. What is the inside diameter of the pipe? Show all work and include units of measure

Answer 1

Answer:

0.10 m

Explanation:

The magnetic flux through the plane is given by

$\Phi = BA$

where

B is the magnetic field intensity

A is the area of enclosed by the pipe

In this problem, we know

$\Phi = 7.3\cdot 10^{-3} Wb$ is the flux

B = 0.90 T is the magnetic field strength

Solving the equation for A, we find the area enclosed by the pipe

$A=\frac{\Phi}{B}=\frac{7.3\cdot 10^{-3} Wb}{0.90 T}=8.1\cdot 10^{-3} m^2$

We know that the area is given by

$A=\pi r^2$

where r is the radius. Solving for r, we find the radius:

$r=\sqrt{\frac{A}{\pi}}=\sqrt{\frac{8.1\cdot 10^{-3} m^2}{\pi}}=0.05 m$

And so the diameter is twice the radius:

$d=2r=2(0.05 m)=0.10 m$