Determine the magnitude and direction of the force between two parallel wires 30 m long and 6.0 cm apart, each carrying 30A in the same direction. Determine the magnitude of the force between two parallel wires.
The concepts used in this problem are magnetic field due to a current carrying wire and the magnetic force. First, derive to expression for force between two wires using the concept of magnetic field due to a current carrying wire and the magnetic force. Then, calculate the force by substituting the values.
Magnetic field due to a current carrying wire:
The expression for magnetic field due to a straight current carrying wire is:
Here, is the magnetic permeability, is the current flowing in the wire and is the distance of point from the wire.
Magnetic force:
The magnetic force is perpendicular to the magnetic field and the direction of current. The magnitude of magnetic force is given by:
Here, is the current, is the velocity, is the magnetic field and is the angle between current and the magnetic field.
The diagram for the given problem is:
The force on wire 2 is:
Substitute for ,
…… (1)
The magnetic field at wire 2 due to current in wire 1 is:
…… (2)
Substitute equation (2) in equation (1).
…… (3)
The expression of force is:
Substitute for , for , for , for and for .
Ans:
The force between two wires is .
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