Three long parallel wires are 3.5 cm from one another. (Looking along them, they

Question

Three long parallel wires are 3.5 cm from one another. (Looking along them, they are at three corners of an equilateral triangle.) The current in each wire is 8.80 A , but its direction in wire M is opposite to that in wires N and P (see the figure).(Figure 1)

Determine the magnitude of magnetic force per unit length on wire M due to the other two.

Express your answer to two significant figures and include the appropriate units.

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Part B

Determine the direction of magnetic force per unit length on wire M due to the other two.

Express your answer to two significant figures and include the appropriate units.

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Part C

Determine the magnitude of magnetic force per unit length on wire N due to the other two.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

given,

distance between the wires = 3.5 cm

current through each wire = 8.8 A

magnetic force per unit length between two current carrying wires = k * I1 * I2 / r

magnetic force per unit length between two wires = 2 * 10^-7 * 8.8 * 8.8 / (3.5 * 10^-2)

magnetic force per unit length between two wires = 4.425 * 10^-4 N/m

since current and distance of all the wires ae same so magnetic force between any two wires will be same

force will be repulsive in nature and angle between to forces will be 60 degree so,

net force per unit length on M = sqrt((4.425 * 10^-4)^2 + (4.425 * 10^-4)^2 + 2 * (4.425 * 10^-4)^2 * cos(60))

net force per unit length on M = 7.664 * 10^-4 N/m

direction of force will be on +y axis that is 90 degree from +x axis

in case of N force due to P will be attractive in nature and force due to M will be repulsive in nature so angle between two forces will be 120 degree so,

net force per unit length on N = sqrt((4.425 * 10^-4)^2 + (4.425 * 10^-4)^2 + 2 * (4.425 * 10^-4)^2 * cos(120))

net force per unit length on N = 4.425 * 10^-4 N/m

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