To determine the relationship between the voltage of the batteries and the strength of the magnetic field produced by the electromagnets, we need to consider that the magnetic field strength \( B \) of an electromagnet is directly related to the current \( I \) flowing through the wire, which, in turn, can be influenced by the voltage \( V \) across the coil.
Using Ohm's Law, \( V = I \cdot R \), we can express the current as \( I = \frac{V}{R} \), where \( R \) is the resistance of the wire, which remains constant for both electromagnets.
If we assume that the resistance \( R \) is the same for both configurations, we can compare the currents produced by each battery:
- For the 1.5-volt battery: \( I_1 = \frac{1.5V}{R} \)
- For the 9-volt battery: \( I_2 = \frac{9V}{R} \)
Now, let's find the ratio of the current produced by the 9-volt battery to that produced by the 1.5-volt battery:
\[ \frac{I_2}{I_1} = \frac{\frac{9V}{R}}{\frac{1.5V}{R}} = \frac{9}{1.5} = 6 \]
This indicates that the current flowing through the wire in the electromagnet powered by the 9-volt battery is 6 times greater than that flowing through the wire in the electromagnet powered by the 1.5-volt battery, assuming the resistance remains constant.
Since the magnetic field strength \( B \) is proportional to the current \( I \), we also conclude that the electromagnet powered by the 9-volt battery will have a magnetic field strength that is 6 times greater than that produced by the 1.5-volt battery.
Therefore, the correct assertion is:
The magnetic field generated by the 9-volt battery will be six times more powerful than that produced by the 1.5-volt battery.