Magnetic Forces/Sources of the Magnetic Field In 1833 Carl Friedrich Gauss and h

Question

Magnetic Forces/Sources of the Magnetic Field In 1833 Carl Friedrich Gauss and his colleague Wilhelm Weber invented one of the first telegraphs. The receiver of the the Weber-Gauss Telegraph consisted of two long straight wires, carrying currents equal in magnitude but oppositely directed. Each was suspended by a pair of light-weight and inelastic threads, 6.0 cm long. When current flowed through the wires the magnetic force exerted between them caused them to move apart. Given that the linear mass density of the wire is A = 40. , find the magnitude of the current in either wire when the angle separating the threads of the device is 16degree. Hint: You will need to write expressions for the magnetic field due to the current in a long straight wire AND the force on a long straight wire, carrying some current, in a uniform and static magnetic field. Take the accleration due to gravity to be 9.82 m

Explanation / Answer

r = 2*L*sin8 = 2*0.06*sin8 = 0.016 m

Fb/L = uo*i*i/(2*pi*r) = (4*pi*10^-7*i^2)/(2*pi*0.016)

Fb = 125*10^-7*i^2*L = T*sin8

Fg = mg = T*cos8

Fb/Fg = tan8 = 125*10^-7*i^2*L/mg = (125*10^-7*i^2)/(0.04*9.82)= 31.823e?6*i^2

i = 66.45A

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