How Does Ampere's Law Calculate Current in a Uniform Magnetic Field?

[ineedhelp5454]

Homework Statement

Along a circular path the magnetic field is measured and is found to be uniform in magnitude and always tangent to the circular path.
If the radius of the path is 0.03 m and B along the path is 1.4e-06 T, use Ampere's law to calculate the magnitude of the conventional current enclosed by the path.

Homework Equations

ampere's law -- integral(B*dl) = mu I

The Attempt at a Solution

i keep getting 3.19e4 A

 

[collinsmark]

Hello ineedhelp5454,

Welcome to Physics Forums!

i keep getting 3.19e4 A

My answer is different by 5 or so orders of magnitude.

Show us your steps and maybe we can help figure out what's going on.

 

[ineedhelp5454]

1.5e-6 * 2 * pi * .03 = 2.87e-7 (left half of ampere's equation)
2.87e-7 = 8.85e-12(mu) * I (right half)
I = 3.19e4

 

[collinsmark]

1.5e-6 * 2 * pi * .03 = 2.87e-7 (left half of ampere's equation)

Is the magnitude of B 1.5 x 10^-6 or 1.4 x 10^-6 T?

2.87e-7 = 8.85e-12(mu) * I (right half)
I = 3.19e4

You're using the vacuum permittivity constant ε₀ = 8.854 x 10^-12 F/m, but you need to use the vacuum permeability constant μ₀= 4π x 10^-7 H/m.

They're not the same thing, but they are related. The speed of light in a vacuum $c = 1/\sqrt{\epsilon_0\mu_0}$

 

[ineedhelp5454]

thanks!