The charges on two spheres are `+7muC` and `–5muC` respectively. They experience a force F. If each of them is given an additional charge of `–2muC`, the new force of attraction will be

Options

A. F
B. `F//2`
C. `F//sqrt3`
D. `2F`

Answer

To solve the problem, we will follow these steps:

### Step 1: Identify the initial charges and the force between them
The initial charges on the two spheres are:
- Charge on sphere 1, \( q_1 = +7 \, \mu C = +7 \times 10^{-6} \, C \)
- Charge on sphere 2, \( q_2 = -5 \, \mu C = -5 \times 10^{-6} \, C \)

The force \( F \) between them can be calculated using Coulomb's law:
\[ F = k \frac{|q_1 \cdot q_2|}{r^2} \]
where \( k \) is Coulomb's constant, and \( r \) is the distance between the charges.

### Step 2: Calculate the initial force
Substituting the values into the formula:
\[ F = k \frac{|(+7 \times 10^{-6}) \cdot (-5 \times 10^{-6})|}{r^2} \]
This simplifies to:
\[ F = k \frac{35 \times 10^{-12}}{r^2} \]

### Step 3: Determine the new charges after adding the additional charge
Each sphere is given an additional charge of \( -2 \, \mu C \):
- New charge on sphere 1, \( q_1' = +7 \, \mu C - 2 \, \mu C = +5 \, \mu C = +5 \times 10^{-6} \, C \)
- New charge on sphere 2, \( q_2' = -5 \, \mu C - 2 \, \mu C = -7 \, \mu C = -7 \times 10^{-6} \, C \)

### Step 4: Calculate the new force with the updated charges
Using Coulomb's law again for the new charges:
\[ F' = k \frac{|q_1' \cdot q_2'|}{r^2} \]
Substituting the new charges:
\[ F' = k \frac{|(+5 \times 10^{-6}) \cdot (-7 \times 10^{-6})|}{r^2} \]
This simplifies to:
\[ F' = k \frac{35 \times 10^{-12}}{r^2} \]

### Step 5: Compare the new force with the initial force
Notice that:
\[ F' = F \]
Thus, the new force of attraction remains the same as the initial force \( F \).

### Final Answer
The new force of attraction will be \( F \).

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