Question

A 260-m length of wire stretches between two towers and carries a 115-a current. determine the magnitude of the force on the wire due to the earth's magnetic field of 5.0 ×10−5t which makes an angle of 80 ∘ with the wire.

Answer 1

The force exerted by a magnetic field of intensity B on a wire of length L is:
$F=ILB \sin \theta$
where I is the current in the wire and $\theta$ is the angle between the wire and the direction of B.
In our problem, the length of the wire is L=260 m, the current is I=115 A, the intensity of the Earth's magnetic field is $B=5.0 \cdot 10^{-5}T$ and the angle between the wire and B is $80^{\circ}$, and by substituting these numbers in the previous expression we can find the magnitude of the force:
$F=(115 A)(260 m)(5.0 \cdot 10^{-5}T)(\sin 80^{\circ})=1.48 N$