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Two large parallel metal plates are [tex]$6.0 \text{ cm}$[/tex] apart. The magnitude of the electric field between them is [tex]$600 \text{ N/C}$[/tex]. What is the potential difference between the plates?

A. [tex]$21 \text{ V}$[/tex]
B. [tex]$18 \text{ V}$[/tex]
C. [tex]$40 \text{ V}$[/tex]
D. [tex]$36 \text{ V}$[/tex]

Note: The charge of an electron is [tex]$1.6 \times 10^{-19} \text{ C}$[/tex].



Answer :

GinnyAnswer
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]

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