Let's solve this problem step-by-step.
1. Convert Distance to Meters:
Given the distance between the plates is [tex]\( 2.5 \, \text{cm} \)[/tex]. We need to convert this distance to meters because the standard unit for electric fields is in meters.
[tex]\[ 2.5 \, \text{cm} = 2.5 \times 10^{-2} \, \text{m} = 0.025 \, \text{m} \][/tex]
2. Calculate the Electric Potential Difference ([tex]\(\Delta V\)[/tex]):
The electric potential difference can be calculated using the formula:
[tex]\[ \Delta V = E \times d \][/tex]
where [tex]\( E \)[/tex] is the electric field, and [tex]\( d \)[/tex] is the distance.
Given [tex]\( E = 800.0 \frac{N}{C} \)[/tex] and [tex]\( d = 0.025 \, \text{m} \)[/tex],
[tex]\[ \Delta V = 800.0 \, \frac{N}{C} \times 0.025 \, \text{m} \][/tex]
[tex]\[ \Delta V = 20.0 \, \text{V} \][/tex]
3. Calculate the Work Done (W):
The work done by the electric field in moving a charge between the plates is given by:
[tex]\[ W = \Delta V \times q \][/tex]
where [tex]\( q \)[/tex] is the charge of the electron.
Given [tex]\( q = 1.602 \times 10^{-19} \, \text{C} \)[/tex]
[tex]\[ W = 20.0 \, \text{V} \times 1.602 \times 10^{-19} \, \text{C} \][/tex]
[tex]\[ W = 32.04 \times 10^{-19} \, \text{J} \][/tex]
4. Express Work Done in Units of [tex]\( 10^{-18} \, \text{J} \)[/tex]:
To express the work in units of [tex]\( 10^{-18} \, \text{J} \)[/tex],
[tex]\[ W = 3.204 \times 10^{-18} \, \text{J} \][/tex]
Thus, the electric potential difference and the work done are:
[tex]\[ \Delta V = 20.0 \, \text{V} \][/tex]
[tex]\[ W = 3.204 \times 10^{-18} \, \text{J} \][/tex]
