From the biot-savart law, which of the following is most useful for estimating the magnetic field from a short current element of length l with current i? from the biot-savart law, which of the following is most useful for estimating the magnetic field from a short current element of length l with current i? μ0i/2πl μ0i2l μ0il/4πr2 μ0i/2l

B = μ₀ I / 2π L

Explanation:

The biot-Savart law has the equation

          B = μ₀ I / 4π ∫ ds * r ^ / r²

Where the vector product gives the direction of the field, ds is taken along the wire length

         ds * r ^ = ds sin θ

         B = μ₀ I / 4π I ds sinθ / r²

r is the distance from current element to the point of interest, to make the calculation easier suppose that the wire is on the x-axis and the calculation point on the Y-axis at a distance L

        ds = dx

We have to write the integral in terms of a single integration variable, if we use geometry, we can write everything in function angle (θ)

      sin θ = L / r

      r = L / sin θ = L csc θ

      tan θ = L / x

      x = L / tan θ

     dx = L csc²θ dθ

substitutions  and calculate

     B = μ₀ I / 4π I (L csc²θ dθ) sinθ / (L cscθ)²  

     B = μ₀ I / 4π I dθ sinθ / a

     B = μ₀ I / 4π I dθ sinθ / a

     B = μ₀ I 4π L (cos T1-cosT2)

If the wire is very long θ1 = 0 t θ2 =π      (cos θ1 -cosθ2) = 2

     B = μ₀ I / 2π L

This is the solution

magnityde and direction