When `10^(14)` electrons are removed from a neutral metal sphere , the charge on it becomes

Options

A. `16 mu C`
B. `-16 mu C`
C. `32 mu C`
D. `-32 mu C`

Explanation

To find the charge on a neutral metal sphere after removing \(10^{14}\) electrons, we can follow these steps:

### Step 1: Understand the charge of one electron
The charge of one electron is given as:
\[ e = -1.6 \times 10^{-19} \text{ coulombs} \]

### Step 2: Calculate the total charge of the removed electrons
If \(10^{14}\) electrons are removed, the total charge removed can be calculated using the formula:
\[ \text{Total charge} = \text{Number of electrons} \times \text{Charge of one electron} \]
Substituting the values:
\[ \text{Total charge} = 10^{14} \times (-1.6 \times 10^{-19}) \]

### Step 3: Perform the multiplication
Calculating the total charge:
\[ \text{Total charge} = -1.6 \times 10^{-5} \text{ coulombs} \]

### Step 4: Convert the charge to microcoulombs
To express this charge in microcoulombs:
\[ -1.6 \times 10^{-5} \text{ coulombs} = -16 \times 10^{-6} \text{ coulombs} = -16 \mu C \]

### Step 5: Determine the charge on the sphere
Since the sphere was initially neutral (0 coulombs), removing negative charge (electrons) results in a positive charge:
\[ \text{Charge on the sphere} = 0 - (-1.6 \times 10^{-5}) = +1.6 \times 10^{-5} \text{ coulombs} = +16 \mu C \]

### Final Answer:
The charge on the metal sphere after removing \(10^{14}\) electrons is:
\[ \text{Charge} = +16 \mu C \]

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