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landishigh
landishigh
Student
College - Freshman

Two long rectilineal conductors, parallel between them, have the distance between them of r=4 cm.An electrical current passes through both of them.

They are attracting each other with the force of F'=mN/m (on unity of length). Which is the value of mechanical work, on unity of length, for reduplication of distance between them?

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Posted by landishigh on Saturday July 4, 2009 at 6:10 AM and tagged with electrical current, long rectilineal conductors, mechanical work, science, unity of length.

Answers:

  1. kjcdb8er
    kjcdb8er Teacher

    eNotes Editor

    The magnetic field from wire one is: B = uI1/2PIr. For electrons moving in wire two, the differential force along dL of the wire felt at distance r is F = I2*dL*B = u*I1*I2*dL/2PIr

    Work is Int(F dr), so W = Int(u*I1*I2*dL/2PIr dr) = (u*I1*I2*dL/2PI)*Int(1/r dr) = K*Int(1/r dr)

    Recalling that Int(1/r dr) = ln(r), the work done moving the wires from 4 cm separation to 8 cm separation is K*ln(8cm/4cm).

    So W/dL = (u*I1*I2/2PI)*ln(2)

    Sources:
    http://www.enotes.com/physic/q-and-a/particle-with-specif...
    http://www.enotes.com/science/q-and-a/an-electron-acceler...

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    Posted by kjcdb8er on Saturday July 4, 2009 at 8:42 AM