A 2 Mev proton is moving perpendicular to a uniform magnetic...

A 2 Mev proton is moving perpendicular to a uniform magnetic field of $2.5$ tesla. The force on the proton is
(a) $3 \times 10^{-10} \mathrm{~N}$
(b) $70.8 \times 10^{-11} \mathrm{~N}$
(c) $3 \times 10^{-11} \mathrm{~N}$
(d) $7.68 \times 10^{-12} \mathrm{~N}$

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Key Concepts

Lorentz Force

This concept describes the force experienced by a charged particle when it moves through a magnetic field. The force is given by the equation F = q(v × B), which means that the force is proportional to the charge, the speed of the particle, and the magnetic field strength. When the velocity is perpendicular to the magnetic field, the magnitude of the force simplifies to F = qvB.

Kinetic Energy-Velocity Relationship

This principle involves converting a particle's kinetic energy into its speed. For a particle of mass m and kinetic energy K, the speed can be found using the relation v = sqrt(2K/m). This conversion is essential when the kinetic energy is given (in this case in electron-volts or megaelectron-volts) and the speed is needed to compute the force.

Unit Conversion for Energy

Since kinetic energy is often provided in units such as megaelectron-volts (MeV), it must be converted to standard SI units (joules) when applying equations in a consistent SI framework. This conversion is crucial for accurate calculations in physics as it ensures all quantities are expressed in compatible units.

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