Question

a square wire of each side l carrier I the magnetic field at the mid-point at the midpoint op the square is​

Answer 1

The magnetic field at the midpoint of the square is 8√2μ₀i/4πl

Given-

• Side of the square wire = l
• Current in the wire = i

We know that magnetic field due to conductor subtending angles θ₁ and θ₂ is

B = μ₀i/4πR ( sin θ₂ - sin θ₁)

Here R is the length from the mid point. So R = L/2

Here θ = 45°

By substituting the values magnetic field due to one side is-

B = μ₀i/4πL/2 [ 1/√2 - (-1/√2)]

B = 2√2 μ₀i/4πL

B due to four sides

B = 4 × 2√2 μ₀i/4πL

B = 8√2μ₀i/4πl