A long wire stretches along the x axis and carries a 3.0-A current to the right

Question

A long wire stretches along the x axis and carries a 3.0-A current to the right (+x). The wire is in a uniform magnetic field B = (0.20i - 0.36j + 0.25k)T. Determine the components of the force on the wire per cm of length. The diagram shows a horizontal 1 5m long copper rod weighing 40.0N suspended at its two ends by two wires attached to the ceiling. It is in a region where the magnetic field is 2.4T pointing into the paper. A current runs in the rod. What must be the direction and magnitude of the current so that tension in each wire is 25N?

Explanation / Answer

7)

F = i ( dl X B)

F/L =3 ( ix (0.2i -0.36j +0.25 k )

F/L = -3( 0.25 j + 0.36 k) N/m

F/L = -0.03( 0.25 j + 0.36 k ) N/cm

8)

for equilibrim

2T = 40+ Fb

2x25 = 40 +Fb

Fb = 10 N downward

so current will in leftward direction

Fb = i L B

10 = i 2.4x1.5

i = 2.78 A ( leftward )

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