Force on a moving charge
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State the direction of the force on a positive charge moving in a magnetic field.
The force is perpendicular to both the velocity of the charge and the magnetic field direction. Can be determined using Fleming's Left-Hand Rule (thumb = force, first finger = field, second finger = conventional current).
Write the formula for the force on a charge moving in a magnetic field and define each term.
F = BQv sin θ, where F is the force (N), B is the magnetic flux density (T), Q is the charge (C), v is the velocity (m/s), and θ is the angle between the velocity and the magnetic field.
What is the Hall voltage, and how does it arise?
The Hall voltage (VH) is the voltage difference created across a conductor perpendicular to both an electric current and a magnetic field. It arises due to the Lorentz force deflecting moving charges to one side of the conductor.
Give the formula for Hall Voltage and define each term.
VH = BI / (ntq), where VH is the Hall voltage, B is the magnetic flux density, I is the current, n is the charge carrier density, t is the thickness of the conductor, and q is the elementary charge.
Describe how a Hall probe is used to measure magnetic flux density.
A Hall probe is placed in the magnetic field. The Hall voltage produced is proportional to the magnetic flux density. By calibrating the Hall probe with known magnetic fields, the unknown field can be determined. V ∝ B
Describe the motion of a charged particle moving in a uniform magnetic field when its velocity is perpendicular to the field.
The particle will move in a circular path. The magnetic force provides the centripetal force required for circular motion.
A proton moves at 3.0 x 10^6 m/s perpendicularly through a uniform magnetic field of 0.50 T. Calculate the magnetic force on the proton.
F = BQv sin θ = (0.50 T)(1.60 x 10^-19 C)(3.0 x 10^6 m/s) sin 90° = 2.4 x 10^-13 N.
Explain how electric and magnetic fields can be used for velocity selection of charged particles.
By applying perpendicular electric and magnetic fields, only particles with a specific velocity will pass through undeflected. The electric force (F = QE) and magnetic force (F = BQv) are balanced when v = E/B.
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