Question

A long wire carrying 4.50 A of current makes two 90° bends, as shown in the figure

The bent part of the wire passes through a uniform 0.238 T magnetic field directed as shown in the figure and confined to a limited region of space.

Part A

Find the magnitude of the force that the magnetic field experts on the the wire.

Part B

Find the direction of the force that the magnetic field experts on the the wire.

Answer 1

The magnetic force on a current carrying conductor \(F=B I L \sin \theta\)

For the horizontal region,

\(F_{H}=0.238 \times 4.5 \times 0.6=0.64 \mathrm{~N}\)

Direction: The magnetic field faces outside the plane of paper, current to the right, hence the force downwards.

For the vertical region,

\(F_{V}=0.238 \times 4.5 \times 0.3=0.32 \mathrm{~N}\)

Direction: The magnetic field faces outside the plane of paper, current to the top, hence the force right.

Total force, \(F=\sqrt{(0.64)^{2}+(0.32)^{2}}=0.72 \mathrm{~N}\)

Direction: Clockwise from the right \(45^{\circ}\)

Answer 2

The final direction angle is wrong... 

You take the inverse tan of Fx/Fy