How many electrons should be removed from a coin of mass `1.6g`, so that it may float in an electric field of intensity of `10^(9)NC^(-1)` directed upward. (take `g= 10m//s^(2)`)

Options

A. `9.8xx10^(7)`
B. `9.8xx10^(5)`
C. `9.8xx10^(3)`
D. `9.8xx10^(1)`

Answer

To determine how many electrons should be removed from a coin of mass 1.6 g so that it may float in an electric field of intensity \(10^9 \, \text{N/C}\) directed upward, we can follow these steps:

### Step 1: Calculate the weight of the coin
The weight \(W\) of the coin can be calculated using the formula:
\[ W = mg \]
where:
- \(m = 1.6 \, \text{g} = 1.6 \times 10^{-3} \, \text{kg}\) (converting grams to kilograms)
- \(g = 10 \, \text{m/s}^2\)

Substituting the values:
\[ W = (1.6 \times 10^{-3} \, \text{kg})(10 \, \text{m/s}^2) = 1.6 \times 10^{-2} \, \text{N} \]

### Step 2: Set up the equilibrium condition
For the coin to float, the upward electric force \(F_e\) must equal the downward weight \(W\):
\[ F_e = W \]
The electric force can be expressed as:
\[ F_e = QE \]
where \(Q\) is the charge on the coin and \(E\) is the electric field intensity.

### Step 3: Relate charge to the number of electrons
The charge \(Q\) can be expressed in terms of the number of electrons \(n\) removed:
\[ Q = n \cdot e \]
where \(e\) is the charge of a single electron, approximately \(1.6 \times 10^{-19} \, \text{C}\).

### Step 4: Substitute into the equilibrium condition
Substituting \(Q\) into the equilibrium condition:
\[ n \cdot e \cdot E = W \]
Rearranging gives:
\[ n = \frac{W}{e \cdot E} \]

### Step 5: Substitute the values
Now we can substitute the values we have:
- \(W = 1.6 \times 10^{-2} \, \text{N}\)
- \(e = 1.6 \times 10^{-19} \, \text{C}\)
- \(E = 10^9 \, \text{N/C}\)

Calculating \(n\):
\[ n = \frac{1.6 \times 10^{-2}}{(1.6 \times 10^{-19})(10^9)} \]
Calculating the denominator:
\[ (1.6 \times 10^{-19})(10^9) = 1.6 \times 10^{-10} \]
Now substituting back:
\[ n = \frac{1.6 \times 10^{-2}}{1.6 \times 10^{-10}} = 10^8 \]

### Step 6: Final answer
Thus, the number of electrons that should be removed from the coin is:
\[ n = 10^8 \]