In: Physics
The unit of current, the ampere, is defined in terms of the force between currents. Two 1.0-meter-long sections of very long wires a distance 2.0m apart each carry a current of 1.0 A
What is the force between them? (If the force between two actual wires has this value, the current is defined to be exactly 1 A.)
The concepts required to solve the given problem is magnetic field due to a current carrying wire and force on a current carrying wire due to magnetic field.
Initially, determine the magnetic field at one wire due to other wire by using expression magnetic field due to a current carrying wire. Then, determine the force on the wire by using magnetic field, length of the wire and current in the wire.
The current carrying wire creates a magnetic field around the wire and the direction of magnetic field around the wire is known by using right hand rule.
The magnitude of magnetic field B due to a current carrying wire at distance r from the wire is given by following expression.
Here, I is the current, and is the permeability.
The magnetic force F on a current carrying wire is given by following expression.
Here, L is the length of the wire.
The magnitude of magnetic field B due to a current carrying wire at distance r from the wire is given by following expression.
Substitute 1.0 A for I, 2.0 for r, and for in the above equation.
The magnetic force F on a current carrying wire is,
Substitute 1.0 A for I, for B, and 1.0 m for L in the above equation.
Ans:
The force between the wires is