Question

3.1. Two metallic rods of length L = 40 cm and unknown linear mass density 1 are suspended from a support using lightweight strings of length s = 8 cm, as shown in the diagram (a) below. The rods are then connected to a circuit in such a way that same current / = 20 A passes through both rods, but flows in opposite directions. When connected in such a way, the rods move away from each other and at equilibrium are separated by a distance r = 2 cm (diagram b). What is the linear mass density 1 (in kg/m) of the rods? \14 marks 3.2. A long straight wire of radius R = 5 mm carries a current, 1o, whose current density, J, varies as a function of distance from its centre, r, according to: r J(r) = ) exp(-2x 10-3 m) (a) Determine the total current passing through the cross-section of the wire (10). 3 marks (b) Use Ampere's law to obtain an expression for the magnetic field magnitude, B, as a function of r, for the region outside the wire (r > R). Hence, evaluate the magnitude of the magnetic 3 marks field generated by this wire 3 mm away from its surface [20 marks total]

Answer 1

(1) L= 0.lim, S=0.08 m , T-20A ,Y: 0.02m 1 ТС 0 Fe = M.I? 23) L Tsince l H ag foom fis: Fp = Usx167x400 40.4 = 1.6x103N 25x6.02 Sinco= 7 = 0.02 2 25 270108 0 -7.18 = 0.125 2. doom EBD: T Since = Fe - 0. ) I Covce mg Dividing een_ (i) by (o) tance = FB = M = FB = 1.6*10-3 gtance 9.8+ tan (7-18°) Ma 1.296X10-3 kg. R = 3.24x10-3 kg/m Lincer man density of sodi.

(3.2) 360) = 100 exp loon) R = 0.005 m T 0.002 dI = J (2) dA = Jx2 ordr To= 100420 1 e soomkorder To= 29x100 le-5000 do To= 2009 (esto) [e- sooo To = -0.48 [295-1] To = 1,153A1 Using ampere's urental hew. & Bode= Mo Tenc. Bx200 - MOTO IB = M.To 200 r=8mm B- u1410-7x10153 _ = 2.883x10-5T 20x 8 x 10²3 B = 2.883610-5T