Question

A high-voltage power line carries a current of 122 A at a location where the Earth's magnetic field has a magnitude of 0.59 G and points to the north, 68 ∘ below the horizontal.

Find the direction of the magnetic force exerted on a 330 mm length of wire if the current in the wire flows horizontally toward the east.

A:force points toward north, 22 ∘∘ above the horizontal

B:force points toward north, 68 ∘∘ above the horizontal

C:force points toward south, 22 ∘∘ above the horizontal

D:force points toward south, 22 ∘∘ below the horizontal

Find the magnitude of the magnetic force exerted on a 330 m length of wire if the current in the wire flows horizontally toward the east. (N)

Find the direction of the magnetic force exerted on a 330 m length of wire if the current in the wire flows horizontally toward the south.

Find the magnitude of the magnetic force exerted on a 330 mm length of wire if the current in the wire flows horizontally toward the south.

Answer 1

Figure shows the coordinate system related to directions like N, S... etc

Current is flowing towards East or Y direction .

Hence current element in vector form    A-m

where unit vector in Y direction.

Magnetic field direction is shown in figure as given in question

Magnetic field in vector form , T

where magnitude of B = 5.9 10-5 T

force acting on current carrying wire is given by

Hence the force is acting in x-z plane as shown below

It can be seen from above figure direction of force is towards North and 68o above horizontal

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Magnitude of force is calculated in previous part, F = 23.8 10-5 N

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when current is flowing towards south then current element in vector form

force acting on current carrying wire is given by

direction of force is towards east

magnitude of force = 23.8 10-5 sin68 = 22 10-5 N