The Definition of B — Question 8

Question 8

A perpendicular-force calibration gives a field scale with consistent SI units

A test charge of magnitude 5.00 nanocoulomb travels perpendicular to an unknown field. Measurements give the linear relation $F=sv$, with $s=2.50\times10^{-9}$ newton second per metre. Use $1$ gauss $=10^{-4}$ tesla.

1. Find B in tesla and gauss.

2. Derive the tesla unit in terms of newtons, amperes and metres, and then in SI base units.

Question 8 - Solution

A perpendicular-force calibration gives a field scale with consistent SI units

(a) Method and calculation

$$s=qB\Rightarrow B=s/q=\frac{2.50\times10^{-9}}{5.00\times10^{-9}}=.500\,\mathrm T.$$$$B=.500/(10^{-4})=5.00\times10^3\,\mathrm{gauss}.$$

(b) Interpretation and further calculation

$$[B]=\frac{\mathrm N}{\mathrm C\,(\mathrm{m/s})}=\frac{\mathrm N}{\mathrm{A\,m}}.$$$$1\,\mathrm T=1\,\mathrm{kg\,A^{-1}\,s^{-2}}.$$

Physical check

The charge must be nonzero and its velocity perpendicular to the field for the slope to equal qB.