Two parallel wires are 4.55 cm apart and carry currents in opposite directions,

Question

Two parallel wires are 4.55 cm apart and carry currents in opposite directions, as shown in the following figure. Find the magnitude and direction of the magnetic field at point P due to two 1.80-mm segments of wire (d?) that are opposite each other and each 8.00 cm from P. (Let d? = 1.80 mm.)

magnitude direction Two parallel wires are 4.55 cm apart and carry currents in opposite directions, as shown in the following figure. Find the magnitude and direction of the magnetic field at point P due to two 1.80-mm segments of wire (de) that are opposite each other and each 8.00 cm from P. (Let de = 1.80 mm.) direction (into the page 12.0 A 8.00 cm 8.00 cm de d2 24.0 A

Explanation / Answer

magnetic field at point P due to upeer segment, B_upper = (mue*I/(4*pi))*(I*dL*sin(theta)/d^2)

here, sin(theta) = (4.55/2)/8

= 0.284375

r = 8 cm = 0.08 m

dL = 1.8 mm = 1.8*10^-3 m

so,

B_upper = (4*pi*10^-7/(4*pi))*(12*1.8*10^-3*0.284375/0.08^2)

= 9.6*10^-8 T

in the simillar way,

magnetic field at point P due to lower segment, B_lower = (mue*I/(4*pi))*(I*dL*sin(theta)/d^2)

= (4*pi*10^-7/(4*pi))*(12*1.8*10^-3*0.284375/0.08^2)

= 9.6*10^-8 T

Bnet = B_upper + B_lower

= 1.92*10^-7 T (in to the page) <<<<<<<----Answer

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