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 in a beam of charged particles is
\( I=\lambda qv \)
where \( \lambda \) is the number of protons per meter, \(q=1.6\times10^{-19}\,\mathrm{C}\), and \(v\) is the average speed.
Solving for the speed,
\( v=\dfrac{I}{\lambda q}=\dfrac{1.6\times10^{-3}}{\left(10^{9}\right)\left(1.6\times10^{-19}\right)}=10^{7}\,\mathrm{m/s} \)
Therefore, the best estimate is \(10^{7}\,\mathrm{m/s}\).
A meter that registers \(0.20~\mathrm{mA}\) at full scale has an internal resistance of \(500~\Omega\). To use this meter as an ammeter with a range of \(0\) to \(1~\mathrm{A}\), one should connect an additional resistance of approximately
Correct Answer: \( \boxed{\mathrm{A}} \)
To convert a meter (galvanometer) into an ammeter, a low-resistance shunt is connected in parallel with the meter so that most of the current bypasses the meter.
At full-scale deflection, the voltage across the meter is
\( V=I_mR_m=(0.20\times10^{-3})(500)=0.10~\mathrm{V} \)
The shunt must carry approximately
\( I_s=1.00-0.00020\approx0.9998~\mathrm{A} \)
Thus, the required shunt resistance is
\( R_s=\dfrac{V}{I_s}\approx\dfrac{0.10}{0.9998}\approx0.10~\Omega \)
Therefore, a resistor of approximately \(0.10~\Omega\) connected in parallel with the meter will extend its range to \(1~\mathrm{A}\).
Hence, the correct answer is (A).
