A solenoid of radius r = 1.25 cm and length l= 32.0 cm has 280 turns and carries

Question

A solenoid of radius r = 1.25 cm and length l= 32.0 cm has 280 turns and carries 12.0 A. Calculate the flux through the surface of a disk-shaped area of radius R = 5.00 cm that is positioned perpendicular to and centered on the axis of the solenoid as in the figure above. agnitude of the magnetic field inside the solenoid? pWb above shows an enlarged end view of the same solenoid. Calculate the flux through the tan area, which is an annulus with an inner radius of a = 0.400 cm and outer radius of b = 0.800 cm. MWb

Explanation / Answer

given

l = 0.32 m

number of turns N = 280

current i = 12 A

radius = r = 1.25 cm = 0.0125 m

magnetic field due too the solenoid = B = uo*(N/L)*i

(a)

area through which flux is present A = pi*r^2

flux = B*A = uo*(N/L)*i*pi*r^2

flux = 4*pi*10^-7*(280/0.32)*12*pi*0.0125^2 = 6.5*10^-6 Nm^2/C

(b)

effective area = A = pi*(b^2-a^2)

flux = B*A = uo*uo*(N/L)*i*pi*(b^2-a^2)

flux = 4*pi*10^-7*(280/0.32)*12*pi*(0.008^2-0.004^2) = 1.98*10^-6 Nm^2/C

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