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

0.10 m

Step-by-step 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=(\Phi)/(B)=(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{(A)/(\pi)}=\sqrt{(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`