help please Two wires (shown on the Figure) are parallel to the z-axis and are c

Question

help please

Two wires (shown on the Figure) are parallel to the z-axis and are carrying currents of I1 = 10.0 A in the -z direction and I2 = 40.0 A in the –z direction. Wire 1 is located at (0 cm, 30 cm) and wire 2 is located at (50 cm, 30 cm). If a third wire, parallel to the first two and carrying a current of 30.0 A in the –z direction, is located at (30 cm, 30 cm), find the magnitude and direction of the magnetic force per unit length on it due to the first two wires.

Explanation / Answer

magnetic force per unit length between two wires

carrying current of i1 and i2 and at a distance of d is given by

F=mu*i1*i2/(2*pi*d)

wires carrying current in the same direction attract each other.

so force between wire 1 and wire 3 is attractive in nature

and along -ve x axis.

force magnitude=4*pi*10^(-7)*10*30/(2*pi*0.3)

=2*10^(-4) N/m

force between wire 2 and wire 3 is attractive in nature

and along +ve x axis.

force magnitude=4*pi*10^(-7)*40*30/(2*pi*(0.5-0.3))

=0.0012 N/m

so total force is along +ve x axis.

and has a magnitude of 0.0012-2*10^(-4)=0.001 N/m

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