Moving Charges And Magnetism

When charged particles move in a magnetic field, they experience a magnetic force that is perpendicular to both their velocity and the magnetic field. This force causes the charged particles to move in circular paths. The magnetic force on a moving charged particle is given by: where:
is the magnetic force,
is the charge of the particle,
is the velocity of the particle, and
is the magnetic field strength.

Since the proton and electron both have charges of equal magnitude ( and respectively), and they are moving with the same velocity in the same magnetic field, they will both experience a centripetal force that causes them to move in circular paths. The radius of the circular path depends on the mass and charge of the particle, but both will follow circular trajectories. Thus, both the electron and the proton move in circular paths in the magnetic field.

Hence, the correct option is (E) : both moves in circular path

Given parameters:

• Magnetic field
• Force
• Charge

Lorentz force equation:

Velocity components:

Solve for velocity:

Thus, the correct option is (C): 50 m/s.

Given parameters:

• Current along z-axis
• Position vector
• Permeability

Biot-Savart Law application: For infinite wire:

Perpendicular distance calculation:

Magnetic field magnitude:

Thus, the correct option is (A): .