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Question 4 a) (10 p) By using the Biot and Savart Law, i.e. dB Hoids sin 0 4π r² (1) written with the familiar notation, find the magnetic field intensity B(0) at the centre of a circular current carrying coil of radius R; the current intensity is i; is the permeability constant, i.e. = 4 x 107 (in SI/MKS unit system). b) Show further that the magnetic field intensity B(z), at an altitude z, above the centre of the current carrying coil, of radius R, is given by B(z): HiR² 2(R²+z²)³/2 c) What is B(0) at z=0? Explain in the light of B(0), you calculated right above. d) Now, we consider a solenoid bearing N coils per unit length. Show that the magnetic field intensity B at a location on the central axis of it, is given by B = μ₁ iN; (4) Note that dz 1 Z (5) 2 2 2 1/2 (R²+z²)³/² R² (R²+z²)¹/² e) What should be approximately the current intensity that shall be carried by a solenoid of 20 cm long, and a winding of 1000 turns, if one proposes to obtain, inside of it, a magnetic field intensity of roughly 0.01 Tesla?