Please help.. Two very long and straight wires are parallel to the z-axis and ca

Question

Please help..

Two very long and straight wires are parallel to the z-axis and carry currents of I1 = 4.0 A and I2=10.0 A in opposite directions. Wire 1 is at the origin while wire 2 is at x = 2.0 m.

a) Find the location of the point where the net magnetic field due to the wires is zero.

b) If a third wire, parallel to the z-axis and carrying a current of I3=30.0 A (same direction as I1) is placed at point P (y = 8.00 m), what are the magnitude and direction of the magnetic force per unit length on wire 1 due to wires 2 & 3 ?

Explanation / Answer

a) B due to 4 A should be equal and opposite to B due to 10 A

4/ (x) = 10/ (x+2)

4x+ 8 = 10x

x= 8/6 = 4/3 m on - x axis from origin

b) distance between P and wire 2= sqroot ( 8^2 + 2^2) = sqroot ( 68)

angle between P and wire 2 = tan^-1 ( 8/2) = 75.96 degree apprx

Fx/l = ( 2 x 10^-7 )( 30x 4) /8 -  (2 x 10^-7 )( 30x 10)sin 75.96 / sqroot ( 68)= 3 x10^-6 - 7.05 x 10^ -6= 4.05 x 10^ -6 N/m

Fy/l = 2.35 x 10^ -6 N/m

angle = tan^-1 ( 2.35/ 4.05) = 30.12 degree

Magnitude of force = 10 ^-6 sqroot ( 4.06 ^2 + 2.35 ^2) = 4.69 x 10^ -6 N/m

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