Homework Help

Two long rectilineal conductors, parallel between them, have the distance between them...

user profile pic

landishigh | Student, College Freshman | eNoter

Posted July 3, 2009 at 10:10 PM via web

dislike 1 like

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?

1 Answer | Add Yours

user profile pic

kjcdb8er | Teacher | (Level 1) Associate Educator

Posted July 4, 2009 at 12:42 AM (Answer #1)

dislike 0 like

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)

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes