Use of SI units and their prefixes：練習問題

A radio station broadcasts at a frequency of \(98.5 \, \text{MHz}\). What is this frequency expressed in standard units \((\text{Hz})\) in standard form?

An equation for the speed \(v\) of a wave on a string is given by \(v = \sqrt{\frac{T}{\mu}}\), where \(T\) is tension and \(\mu\) is mass per unit length. What are the SI base units for \(\mu\)?

The Stefan-Boltzmann law states that the luminosity \(L\) of a black body is related to its surface area \(A\) and absolute temperature \(T\) by \(L = \sigma A T^4\), where \(\sigma\) is the Stefan-Boltzmann constant. What are the SI base units for \(\sigma\)?

Which of the following SI prefixes represents a multiplier of \(10^{-12}\)?

Magnetic flux density \(B\) can be defined using the magnetic force equation \(F = B I L\), where \(I\) is current and \(L\) is length. What are the SI base units for magnetic flux density?

Express a length of \(1.5 \text{ nm}\) in metres using standard form.

The Young modulus E of a sample of steel is measured as \(210 \, \text{GPa}\). Express this value in terms of the SI base units \(\text{kg}\), \(\text{m}\), and \(\text{s}\), using standard form.

Convert the energy value of \(1.0 \text{ kW h}\) (kilowatt-hour) into the fundamental SI unit of energy, the joule (\(\text{J}\)).

A student is asked to record three physical quantities and convert them using SI prefixes.

Convert the following measurements, expressing the final answer in standard form where necessary and using appropriate prefixes where requested:

(a) A capacitor has a capacitance of \(470 \, \mu\text{F}\). Express this value in farads (\(\text{F}\)) using standard form.
(b) The electrical energy \(E\) stored in a capacitor is given by \(E = \frac{1}{2}CV^2\), where \(V\) is the potential difference. Calculate the energy stored when \(V = 15.0 \, \text{V}\) and \(C = 470 \, \mu\text{F}\). Express your answer in millijoules (\(\text{mJ}\)).
(c) The force \(F\) on a current-carrying conductor in a magnetic field is given by \(F = BIL\), where \(B\) is the magnetic flux density, \(I\) is the current, and \(L\) is the length. Determine the SI base units of \(B\).