A deuteron (the nucleus of an isotope of bydrogen) has a mass of 3.34 ×10^-27 kg and a charge of

step 1 M is equal to 3 .34 times 10 to the power minus 27 kilogram and charge Q is equal to plus E. Wel

A deuteron (the nucleus of an isotope of bydrogen) has a...

A deuteron (the nucleus of an isotope of bydrogen) has a mass of $3.34 \times 10^{-27} \mathrm{kg}$ and a charge of $+e .$ The deuteron travels in a circular path with a radius of 6.96 $\mathrm{mm}$ in a magnetic field with magnitude 2.50 $\mathrm{T}$ . (a) Find the speed of the deuteron. (b) Find the time required for it to make half a revolution. (c) Through what to potential difference would the deuteron have to be accelerated to acquire this speed?

Key Concepts

Lorentz Force

The Lorentz force is the fundamental force acting on a charged particle moving in a magnetic field. When the particle’s velocity is perpendicular to the magnetic field, this force has a magnitude equal to the product of the charge, the speed of the particle, and the magnetic field strength, and it always acts perpendicular to the motion. This causes the particle to move in a circular path, with the magnetic force providing the necessary centripetal force for this motion.

Uniform Circular Motion

Uniform circular motion describes the motion of an object traveling at a constant speed along a circular path. Key parameters include the radius of the circle, the period (the time for one complete revolution), and the relationship between the centripetal force and the mass and velocity of the particle. In scenarios involving charged particles in magnetic fields, the centripetal force is provided by the magnetic Lorentz force.

Energy Conversion and Particle Acceleration

In processes where charged particles are accelerated through a potential difference, the electrical potential energy is converted into kinetic energy. The relationship is given by equating the gain in kinetic energy to the product of the charge and the potential difference. This concept is essential for understanding how particles achieve sufficient speeds before entering a magnetic field, thereby linking the accelerator’s potential difference to the speed of the particle.

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