Question

When $ 10^{19} $ electrons are removed from a neutral metal plate, the electric charge on it is

• A. \( -1.6 \, \text{C} \)
• B. \( +1.6 \, \text{C} \)
• C. \( 10^{-19} \, \text{C} \)
• D. \( 10^{19} \, \text{C} \)

Hint:

When electrons are removed, the plate becomes positively charged. The total charge is calculated by multiplying the number of electrons removed by the charge of one electron.

Answer 1

The Correct Option is B

The charge of one electron is \( e = 1.6 \times 10^{-19} \, \text{C} \). 
When electrons are removed from a neutral metal plate, the charge on the plate becomes positive because the removal of negatively charged particles leads to an excess of positive charge. 
The total charge removed from the metal plate can be calculated by: \[ Q = n \times e \] where: 
- \( Q \) is the total charge, 
- \( n = 10^{19} \) is the number of electrons removed, 
- \( e = 1.6 \times 10^{-19} \, \text{C} \) is the charge of one electron. Substituting the values: \[ Q = 10^{19} \times 1.6 \times 10^{-19} \, \text{C} = 1.6 \, \text{C} \] 
Thus, the charge on the plate is \( +1.6 \, \text{C} \). Therefore, the correct answer is: \[ \text{(2) } +1.6 \, \text{C} \]

Answer 2

To determine the electric charge on a metal plate after removing \(10^{19}\) electrons, we need to calculate the total charge that has been removed. The charge of a single electron is \( -1.6 \times 10^{-19} \, \text{C} \). When electrons are removed, negative charge is effectively taken away, leaving a positive charge on the plate. The total charge removed (\( Q \)) is calculated by multiplying the charge of a single electron by the number of electrons removed:

\[ Q = 10^{19} \times (-1.6 \times 10^{-19} \, \text{C}) \]

Simplifying this:

\[ Q = -1.6 \times 10^{0} \, \text{C} \]

\[ Q = -1.6 \, \text{C} \]

Since we have removed electrons, this negative charge being removed results in a positive charge on the plate of:

\[ Q = +1.6 \, \text{C} \]

The correct answer is thus \( +1.6 \, \text{C} \).