Force between two identical spheres charged with same charge is F. If `50%` charge of one sphere is transferred to the other sphere then the new force will be :-

Options

A. `(3)/(4)F`
B. `(3)/(8)F`
C. `(3)/(2)F`
D. none of these

Explanation

To solve the problem, we need to analyze the situation step by step.

### Step 1: Understand the initial force between the two spheres
Let the charge on each sphere be \( q \). The force \( F \) between two charged spheres is given by Coulomb's law:

\[ F = k \frac{q \cdot q}{L^2} = k \frac{q^2}{L^2} \]

where \( k \) is Coulomb's constant and \( L \) is the distance between the centers of the spheres.

### Step 2: Determine the new charges after transferring 50% of one charge
If 50% of the charge from one sphere is transferred to the other, the new charges on the spheres will be:

- Charge on the first sphere after transfer: \( q - \frac{q}{2} = \frac{q}{2} \)
- Charge on the second sphere after transfer: \( q + \frac{q}{2} = \frac{3q}{2} \)

### Step 3: Calculate the new force between the spheres
Now, we can calculate the new force \( F' \) between the two spheres using the new charges:

\[ F' = k \frac{\left(\frac{q}{2}\right) \cdot \left(\frac{3q}{2}\right)}{L^2} \]

### Step 4: Simplify the expression for the new force
Substituting the values into the equation gives:

\[ F' = k \frac{\frac{3q^2}{4}}{L^2} = \frac{3}{4} \left(k \frac{q^2}{L^2}\right) = \frac{3}{4} F \]

### Step 5: Conclusion
Thus, the new force \( F' \) between the two spheres after transferring 50% of the charge from one sphere to the other is:

\[ F' = \frac{3}{4} F \]

### Final Answer
The new force will be \( \frac{3}{4} F \).

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