(a) Find the resultant magnetic force exerted by the long wire on the square cur

Question

(a) Find the resultant magnetic force exerted by the long wire on the square current loop in the figure below if I1 = 8.64 A and I2 = 4.08 A. The edge length of the square is 19.8 cm, and the distance from the long wire to the closest edge of the loop is 4.95 cm.

magnitude

magnitude

Find the resultant magnetic force exerted by the long wire on the square current loop in the figure below if I_1=8.64 A and I_2=4.08 A. The edge length of the square is 19.8 cm, and the distance from the long wire to the closest edge of the loop is 4.95 cm. magnitude direction Find the magnetic torque on the current loop. magnitude direction

Explanation / Answer

magnetic field at a distance r due to long wire = B = uo*I1/(2*pi*r)

magnetic force on square = B*I2*L

on the vertical length at the near end F1 = -B1*I2*L = -uo*I1*I2*L/(2*pi*r)

r = 0.0495 cm

L = 0.198 m

on the vertical length at the farther end

F2 = B2*I2*L = uo*I1*I2*L/(2*pi*(r+L))

for horizantal parts Fnet = 0

Fnet = F1 + F2

Fnet = (uo*I1*I2*L/(2*pi))*( -1/r + 1/(r+L) )

Fnet = (4*pi*10^-7*8.64*4.08*0.198/(2*pi))*(-(1/0.0495) + (1/(0.0495+0.198)))

Fnet = -2.25*10^-5 N

magnitude = 2.256*10^-5 N

direction towards the wire

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