The magnitude of the force that the magnetic field of the current exerts on the electron is approximately 3.82×10^−16 N.
The force exerted by the magnetic field of a current-carrying wire on a moving electron is given by the formula F=Bqv, where F is the force, B is the magnetic field strength, q is the charge of the electron, and v is its velocity. In this scenario, the electron is moving toward the wire, which creates a magnetic force due to the interaction with the magnetic field generated by the current in the wire.
To calculate the force, one needs to determine the magnetic field strength at the location of the electron. For a long, straight current-carrying wire, the magnetic field strength at a distance r from the wire is given by B= μ0I/2πr, where μ0 is the permeability of free space and I is the current.
Substituting the given values and solving for force, F=Bqv, one obtains a force magnitude of approximately 3.82×10^−16 N. This indicates the strength of the magnetic force exerted on the electron by the current-carrying wire when the electron is at a distance of 4.30 cm and moving with a speed of 5.90×10^4 m/s toward the wire.