Ampere's Law Formula

Ampere's law allows us to calculate magnetic fields from the relation between the electric currents that generate this magnetic fields. It states that for a closed path the sum over elements of the component of the magnetic field is equal to electric current multiplied by the empty's permeability.

Integration over the closed path of (magnetic field . infenitesimal segment of the integration path) = empty's permeability * enclosed electric current by the path

The equation is:

∫B.dl = μ₀I

Where:

B: magnetic field

dl: infinitesimal segment of the integration path

μ₀: empty's permeability

I: enclosed electric current by the path

Ampere's Law Formula Questions:

1) Determine the magnetic field strength a distance r away from an infinitely long current carrying wire using the Ampere's law.

Answer:

From the Ampere's law, we solve the integral

∫B.dl = B∫dl = B2πr

Then,

B2πr = μ_oI

B = μ_oI / 2πr

2) Determine the magnetic field strength anywhere inside a solenoid with n turns per unit length using the Ampere's law

Answer:

Solving the integral we have

∫B.dl = B∫dl = Bl

Now the current inside the solenoid is

I = ni , where n is number of turns

We define N as N = n / l

So, B = μ₀ni / l

Finally, B = μ₀Ni