1. (a) According to the Biot-Savart law, the element of magnetic induction field, dB(r), at position, r, that arises fro

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1 A According To The Biot Savart Law The Element Of Magnetic Induction Field Db R At Position R That Arises Fro 1 (102.13 KiB) Viewed 44 times

1. (a) According to the Biot-Savart law, the element of magnetic induction field, dB(r), at position, r, that arises from an element of current, j(r'), at position, r', is given by dB(r) Ho j(r') x (r - r') dr' 4T Ir-r' (i) Sketch the vector field j(r') x (r-r') around a long, thin, straight wire, which carries a steady current, with current density, j(r'), and passes through the coordinate origin. Show clearly each of these vectors and the direction of the field. [4 marks] (ii) Show that an element of the B field arising from a current distribution j(r') is also H. Vxj(r') dB(r) dr' 41 Ir-r' Hint: Use the identity Vx (wa) = x V xa + xa and the gradient - V = Ir-r'l Ir-r'3 Ir-r'l [6 marks] (b) (1) The B field due to a current distribution may be expressed as B(r) = 7 x A(r). Deduce the form of A(r) from the expression for dB(r) in part (a) (ii) above. [3 marks] (ii) Explain briefly why B(r) is not uniquely determined by A(r). [4 marks]