List three factors that can increase the strength of an electromagnet and calculate the height of water in a barometer if the mercury level is 67cm.

The atmospheric pressure ($P_{atm}$) is the same for both barometers.
$$
P_{atm} = \rho_{\text{mercury}} g h_{\text{mercury}} = \rho_{\text{water}} g h_{\text{water}}
$$

$$
\rho_{\text{mercury}} h_{\text{mercury}} = \rho_{\text{water}} h_{\text{water}}
$$

$h_{\text{mercury}} = 67 \text{ cm} = 0.67 \text{ m}$  
$\rho_{\text{water}} = 1000 \text{ kg/m}^3$  
$\rho_{\text{mercury}} = 13600 \text{ kg/m}^3$

$$
13600 \text{ kg/m}^3 \times 0.67 \text{ m} = 1000 \text{ kg/m}^3 \times h_{\text{water}}
$$
$$
h_{\text{water}} = \frac{13600 \text{ kg/m}^3 \times 0.67 \text{ m}}{1000 \text{ kg/m}^3}
$$
$$
h_{\text{water}} = \frac{9112}{1000} \text{ m}
$$
$$
h_{\text{water}} = \boxed{9.112 \text{ m}}
$$

**ii)** A force pump must be used instead of a lift pump to raise water from a deep well over $10 \text{ m}$ because a lift pump relies on atmospheric pressure, which can only push water up to a maximum height of approximately $10.3 \text{ m}$ (at sea level). A force pump, however, can exert a positive pressure to push water to much greater heights, overcoming this atmospheric pressure limit.