Question

Heavy ion radiotherapy is a relatively new cancer treatment that uses high energy
beams of ions to destroy cancer cells. Carbon nuclei having a mass of 1.99 × 10−26 kg
and a charge of +6e (corresponding to the most common isotope of carbon, with six
protons and six neutrons) are accelerated at 2.60×102 m/s2
. Determine the magnitude
of the electric field required to produce this acceleration, assuming that this field is
constant over the region where the ions are being accelerated.

Answer 1

Answer on Question #65020, Physics / Other

Heavy ion radiotherapy is a relatively new cancer treatment that uses high energy beams of ions to destroy cancer cells. Carbon nuclei having a mass of $1.99 \times 10^{-26} \, \mathrm{kg}$ and a charge of $+6\mathrm{e}$ (corresponding to the most common isotope of carbon, with six protons and six neutrons) are accelerated at $2.60 \times 10^{2} \, \mathrm{m/s}^{2}$. Determine the magnitude of the electric field required to produce this acceleration, assuming that this field is constant over the region where the ions are being accelerated.

Solution:

If the electric field at a particular point is known, the force a charge q experiences when it is placed at that point is given by :

$$F = q E$$

The Newton's second law

$$m a = F$$

Thus,

$$m a = q E$$ $$E = \frac {m a}{q}$$

Substituting,

$$E = \frac {(1.99 \times 10^{-26} \, \mathrm{kg}) \times (2.60 \times 10^{2} \, \mathrm{m/s}^{2})}{6 \times 1.6 \times 10^{-19} \, \mathrm{C}} = 5.4 \times 10^{-6} \, \mathrm{N/C}$$

Answer: $5.4 \times 10^{-6} \, \mathrm{N/C}$

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