A long solenoid with 12.8 turns/cm and a radius of 8.91 cm carries a current of

Question

A long solenoid with 12.8 turns/cm and a radius of 8.91 cm carries a current of 21.9 mA. A current of 9.60 A exists in a straight conductor located along the central axis of the solenoid. (a) At what radial distance from the axis in centimeters will the direction of the resulting magnetic field be at 51.8

Explanation / Answer

Bs and Bw are B fields at point P due to solenoid and wire respectively Bs is along the axis of solenoid and Bw is perpendicular to axis B(magnetic field) at point P, 51.8 degrees to Bs => Bw = Tan( 51.8 ) * Bs =1.27 therefore Bw = 1.27Bs -- (1) Bs = 4*PI E-7*0.219*12.80 Bw = 4*PI E-7*9.6/(2*PI*d) According to the equation (1) d = 5.45 cms (b) B = Bs * sec(51.8) = 0.4533*4*PI E-7*Tesla-m/A *[1*E-2 turns/m] = 5.693 Tesla

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