Unit 11: Electric Circuits
Weightage : 15–18%
A narrow beam of protons produces a current of \(1.6\times10^{-3}~\mathrm{A}\). There are \(10^{9}\) protons in each meter along the beam. Of the following, which is the best estimate of the average speed of the protons in the beam?
Correct Answer: \( \boxed{\mathrm{D}} \)
The current is the amount of charge passing a point each second:
\( I=\lambda qv, \)
where \( \lambda \) is the number of protons per meter, \(q=1.6\times10^{-19}~\mathrm{C}\) is the charge of one proton, and \(v\) is the average speed.
Rearranging,
\( v=\dfrac{I}{\lambda q}. \)
Substituting the given values,
\( v=\dfrac{1.6\times10^{-3}}{\left(10^{9}\right)\left(1.6\times10^{-19}\right)} =\dfrac{1.6\times10^{-3}}{1.6\times10^{-10}} =10^{7}~\mathrm{m/s}. \)
Therefore, the best estimate of the average speed of the protons is \(10^{7}~\mathrm{m/s}\).
Therefore, the correct answer is (D).
