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A magnetic field of 100 G (1 G = 10^(-4) T) is required which is uniform in a region of linear dimension about 10 cm and area of cross-section about 10^(-3) m^(2). The maximum current-carrying capacity of a given coil of wire is 15 A and the number of turns per unit length that can be wound round a core is at most 1000 turns m^(-1). Suggest some appropriate design particulars of a solenoid of the required purpose. Assume the core is not ferromagnetic. |
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Answer» SOLUTION :We know that magnetic field inside a solenoid is given by `B = (mu_0 N I)/(L)` For field to be uniform in a region of length 10 cm, the total length of the solenoid shouldbe much greater. With this IDEA in mind we suggest a PARTICULAR design of a solenoid as Length `l = 1 m`, radius = 2 cm, total number of turns N = 800 and current I = 10 A Then the magnitude field `B = (mu_0 N I)/(l) = (4 pi xx 10^(-7) xx 800 xx 10)/(1) = 10^(-2) T " or " 10^(2) G` These particulars are not unique. We may have other suitable parameters [l = 0.5 m, N = 400, radius R = 4 cm and current l = 10 A] which may also give the magnetic field of the same order. |
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