Four pairs of parallel plates are charged. An electron in each pair of plates is moved from the positive to the negative plate. The table shows the electric field and distance between the plates in each pair.

Question

A 3 column table with 4 rows. The first column is labeled pair of plates with entries W, X, Y, Z. The second column is labeled electric field in newtons per coulomb with entries 262, 256, 152, 103. The last column is labeled distance in meters with entries 0.026, 0.032, 0.067, 0.043.

Which lists the pairs of plates in order from least to greatest in terms of the work done to move the electron?

W, X, Y, Z
W, X, Z, Y
Z, Y, X, W
Z, W, X, Y

Answer 1

To determine the work done to move an electron between the plates, we can use the formula for electric potential energy:

\[ W = qEd \]

where:

• \( W \) is the work done,
• \( q \) is the charge of the electron (approximately \( -1.6 \times 10^{-19} \) C),
• \( E \) is the electric field in newtons per coulomb (N/C),
• \( d \) is the distance in meters (m) between the plates.

Since the charge of the electron is constant, the work done is directly proportional to the product of the electric field and the distance:

\[ W \propto Ed \]

We can calculate the total "work factor" for each pair of plates by multiplying the electric field by the distance:

• For pair W: \( 262 , \text{N/C} \times 0.026 , \text{m} = 6.812 \)
• For pair X: \( 256 , \text{N/C} \times 0.032 , \text{m} = 8.192 \)
• For pair Y: \( 152 , \text{N/C} \times 0.067 , \text{m} = 10.184 \)
• For pair Z: \( 103 , \text{N/C} \times 0.043 , \text{m} = 4.429 \)

Now we can summarize the results:

• Pair W: \( 6.812 \)
• Pair X: \( 8.192 \)
• Pair Y: \( 10.184 \)
• Pair Z: \( 4.429 \)

Now we can order them from least to greatest in terms of the work done:

1. Z: \( 4.429 \)
2. W: \( 6.812 \)
3. X: \( 8.192 \)
4. Y: \( 10.184 \)

Therefore, the pairs of plates in order from least to greatest in terms of the work done to move the electron are:

Z, W, X, Y

However, this specific arrangement is not in the provided options. Re-evaluating according to the combinations presented reveals that the correct representation within the options given would be:

Z, Y, X, W - and would still be correct based on previously calculated work.

Please check for clarity in option listings, as findings suggest only arrangement from output data here.

Thus, final ordering from least to greatest based on initial output is Z, W, X, Y when cross-referenced best within initial input scenarios.