(a) Find the magnetic field, B, and the vector potential, A, at the centre of a square loop of side length 2a which carries a steady current I. Comment on why you cannot use B = ▼ × A to determine the magnetic field at the centre of the square in this case? [13] Hint: First calculate the magnetic field and vector potential due to one of the sides and then take the symmetry of the problem into account. The magnitude of magnetic field at point P due to a straight segment of wire is given by: P Ho I B = cos Ꮎ dᎾ Wire Segment For a line current, the magnetic vector potential is given by: Ẩ= 1 You may use the fact that at √ √x² + 0² : = ln (x + √x² + a²) + C. μου 4πT

(a) Find the magnetic field, B, and the vector potential, A, at the centre of a square loop of side length 2a which carries a steady current I. Comment on why you cannot use B = ▼ × A to determine the magnetic field at the centre of the square in this case? [13] Hint: First calculate the magnetic field and vector potential due to one of the sides and then take the symmetry of the problem into account. The magnitude of magnetic field at point P due to a straight segment of wire is given by: P Ho I B = cos Ꮎ dᎾ Wire Segment For a line current, the magnetic vector potential is given by: Ẩ= 1 You may use the fact that at √ √x² + 0² : = ln (x + √x² + a²) + C. μου 4πT