An electron is accelerated from rest by a potential...

An electron is accelerated from rest by a potential difference of $350 \mathrm{~V}$. It then enters a uniform magnetic field of magnitude $200 \mathrm{mT}$ with its velocity perpendicular to the field. Calculate (a) the speed of the electron and (b) the radius of its path in the magnetic field.

An electron is accelerated from rest by a potential difference of $350 \mathrm{~V}$. It then enters a uniform magnetic field of magnitude $200 \mathrm{mT}$ with its velocity perpendicular to the field. Calculate
(a) the speed of the electron and (b) the radius of its path in the magnetic field.

Key Concepts

Lorentz Force

The Lorentz force is the force exerted on a charged particle moving in a magnetic field, expressed as F = qvB when the velocity is perpendicular to the magnetic field. This force is responsible for altering the direction of the particle’s motion without doing work on it, leading to circular motion.

Circular Motion in a Uniform Magnetic Field

When a charged particle enters a magnetic field with a velocity that is perpendicular to the field lines, the magnetic force acts as a centripetal force, causing the particle to travel in a circular path. The radius of this circular path can be determined by equating the magnetic force to the centripetal force required for circular motion.

Electric Potential Difference and Energy Conversion

This concept involves understanding that a charged particle, such as an electron, gains kinetic energy when accelerated by an electric potential difference. The work done on the particle (equal to the charge multiplied by the voltage) is converted into kinetic energy, which is then used to calculate the speed of the particle.

Kinetic Energy

Kinetic energy is the energy a body possesses due to its motion, given by the formula (1/2)mv². In problems involving acceleration by electrical potential difference, the gained kinetic energy of a charged particle is determined by equating the electrical work to its kinetic energy, allowing one to solve for the velocity.

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