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 8.80A , but its direction in wire M is opposite to that in wires N and P (see the figure). Determine the magnitude of magnetic force per unit length on wire M due to the other two. Determine the direction of magnetic force per unit length on wire M due to the other two. Determine the magnitude of magnetic force per unit length on wire N due to the other two. Determine the direction of magnetic force per unit length on wire N due to the other two (counterclockwise from the positive x position). Determine the magnitude of magnetic force per unit length on wire P due to the other two. Determine the direction of magnetic force per unit length on wire P due to the other two (counterclockwise from the positive x position).

Explanation / Answer

force between two parallel wires is given by F = u0i1i2L/2pid

where u0 = constnat = 4pi*10^-7 H/m,

i1, i2 are the currents ,

L s the length o the wire,

d is the distqance between these two wires

if current are in same directiion, there exists , they exert attractive force on each other

and

if currents are in opposite direction, they exert repulsive force

so force between N and M is F1 = 4*3.14 e-7 * 8.8 * 8.8 /(2*3.14 * 0.035)

F1/L = 4.42 e -4 N/m

similarly Force beteen M and p is

F2/L = 4.42 e -4 N/m

angle between them is tna theta = 1

theta   = 45 deg ---<<<<<<<<<<<direction

so

FNet ^2 = ( F1^2 +F2^2 +(2F1F2 cos theta)

Fnet^2 = 4.42 ^2   + 4.42^2   + (2*4.42*4.42* cos 45)

Fnet = 8.167 *10^-4 N/m -----------------<<<<<<<<Answer

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