To determine the potential difference between two large parallel metal plates separated by a given distance with a known electric field, we use the relationship between electric field (E), distance (d), and potential difference (V). The formula that relates these quantities is:
[tex]\[ V = E \cdot d \][/tex]
where:
- \( V \) is the potential difference in volts (V),
- \( E \) is the electric field in newtons per coulomb (N/C),
- \( d \) is the distance between the plates in meters (m).
Here are the given values:
- The distance \( d \) between the plates is \( 6.0 \text{ cm} \).
- The electric field \( E \) is \( 600 \text{ N/C} \).
First, we need to convert the distance from centimeters to meters because the standard unit for distance in this formula is meters.
[tex]\[ 6.0 \text{ cm} = 6.0 \text{ cm} \times \frac{1 \text{ m}}{100 \text{ cm}} = 0.06 \text{ m} \][/tex]
Next, we substitute the known values into the formula:
[tex]\[ V = E \cdot d \][/tex]
[tex]\[ V = 600 \text{ N/C} \cdot 0.06 \text{ m} \][/tex]
Now, we perform the multiplication:
[tex]\[ V = 600 \cdot 0.06 \][/tex]
[tex]\[ V = 36.0 \][/tex]
So, the potential difference between the plates is \( 36.0 \text{ V} \).
Among the given choices:
[tex]$21 \text{ V}, 18 \text{ V}, 40 \text{ V}, 36 \text{ V}$[/tex],
The correct answer is:
[tex]\[ \boxed{36 \text{ V}} \][/tex]
