(II) A 1.5-MeV (kinetic energy) proton enters a 0.30-T field, in a plane perpendicular to the fi

step 1 Okay, so step one will be to equate the magnetic force, maximum force from the magnetic field F

(II) A 1.5-MeV (kinetic energy) proton enters a 0.30-T...

Key Concepts

Centripetal Force in Uniform Circular Motion

When the magnetic force acts as a centripetal force, it causes the charged particle to move in a circular path. The centripetal force required to keep an object moving in a circle of radius r is given by m*v^2/r, where m is the mass of the particle and v is its velocity. Equating the magnetic force to the centripetal force (qvB = m*v^2/r) leads to the expression for the radius of the circular path, r = m*v/(qB). This relation is a key concept when analyzing circular motion in magnetic fields.

Magnetic Force on a Charged Particle

When a charged particle moves through a magnetic field, it experiences a force described by the Lorentz force law. This force acts perpendicular to both the particle’s velocity and the magnetic field, and its magnitude is given by F = qvB, where q is the charge, v is the velocity, and B is the magnetic field. This concept is fundamental in understanding how magnetic fields influence the motion of charged particles.

Kinetic Energy and Velocity Conversion

The kinetic energy of a particle, given by K = 1/2*m*v^2, is directly related to its velocity. When a particle's kinetic energy is known, its speed can be determined by rearranging the equation to v = sqrt(2K/m). This concept is crucial in scenarios where the velocity of the particle is not directly provided but must be computed from the energy, thereby allowing further calculations related to its motion in a magnetic field.

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