Question

Current sheet - surface currents can be approximated numerically by a tiling of quadrilaterals like the one shown below, with current I flowing parallel to the top and bottom edges, from left to right. Let the vector ℓ=ℓ+​=ℓ−​run along either the top or bottom edge, parallel to the current; w=w−​=w+​from bottom to top along the left or right edge; and r₀ be the point at the center of the parallelogram as shown in the diagram. a) Parametrize the surface of the parallelogram as r′(s,t), with the top and bottom edges are at t=+1/2 and −1/2​, and the left and right edges are at s=+1/2​ and −1/2​ respectively. b) Write down the Biot-Savart integral for the magnetic field in terms of integration parameters s,t and constants r₀​≡r−r₀′​,ℓ, and w.

Answer 1

The Biot-Savart law can be used to calculate the magnetic field produced by a current. In this case, we need to parametrize the surface of the parallelogram and write down the Biot-Savart integral for the magnetic field in terms of integration parameters and constants.

Step-by-step explanation:

The Biot-Savart law is used to calculate the magnetic field produced by a current. In this case, we need to parametrize the surface of the parallelogram as r'(s,t).

The top and bottom edges are at t = +1/2 and -1/2, and the left and right edges are at s = +1/2 and -1/2.

The Biot-Savart integral for the magnetic field can be written as an integration of the parameters s, t, and the constants r₀, ℓ, and w.