Source: High school physics (Chinese)
Problem
In the experiment of Figure to measure magnetic flux density, a coil of $N = 9$ turns hangs from the right pan of a balance with its lower edge of length $l = 10.0$ cm immersed in the magnetic field. When the coil carries a current $I = 0.10$ A, a mass $m = 8.78$ g must be added to the pan to restore balance. Determine the magnetic flux density $B$. (Take $g = 9.8\ \text{m}/\text{s}^2$.)
Only the lower edge of the coil lies inside the magnetic field; the other parts of each turn are outside the field (or experience canceling forces). The Ampere force on $N$ turns of length $l$ carrying current $I$ has magnitude
$$F = NBIl.$$At balance this force equals the added weight:
$$NBIl = mg \quad\Longrightarrow\quad B = \frac{mg}{NIl}.$$Substituting $m = 8.78\times10^{-3}$ kg, $g = 9.8\ \text{m}/\text{s}^2$, $N = 9$, $I = 0.10$ A, $l = 0.10$ m:
$$B = \frac{8.78\times10^{-3}\times 9.8}{9\times 0.10\times 0.10} = \frac{0.0860}{0.0900} \approx 0.96\ \text{T}.$$