Force of attraction between two point charges `Q` and `-Q` separated by `d metre is F_(e )`. When these charges are placed on two identical spheres of radius `R = 0.3 d` whose centres are `d metre` apart , the force of attraction between them is

Options

A. greater than `F_(e )`
B. equal to `F_(e )`
C. less than `F_(e )`
D. none of these

Explanation

To solve the problem of finding the force of attraction between two identical spheres with charges \( Q \) and \( -Q \), we can follow these steps:

### Step 1: Understand the Initial Situation
Initially, we have two point charges \( Q \) and \( -Q \) separated by a distance \( d \). The force of attraction between these point charges is given by Coulomb's Law:
\[ F_e = k \frac{|Q \cdot (-Q)|}{d^2} = k \frac{Q^2}{d^2} \]
where \( k \) is Coulomb's constant.

### Step 2: Analyze the New Situation with Spheres
Now, the charges are placed on two identical spheres with radius \( R = 0.3d \). The centers of these spheres are still \( d \) meters apart.

### Step 3: Determine the Effective Distance
When the charges are distributed over the surfaces of the spheres, the effective distance between the charges is not simply \( d \). Instead, we need to consider the distance from the surface of one sphere to the surface of the other sphere.

The distance from the center of one sphere to the center of the other sphere is \( d \), and since each sphere has a radius of \( 0.3d \), the distance between the surfaces of the spheres is:
\[ d - 2R = d - 2(0.3d) = d - 0.6d = 0.4d \]

### Step 4: Calculate the New Force of Attraction
Now, we can use Coulomb's Law again to find the new force of attraction \( F \) between the two spheres:
\[ F = k \frac{|Q \cdot (-Q)|}{(0.4d)^2} = k \frac{Q^2}{(0.4d)^2} = k \frac{Q^2}{0.16d^2} \]

### Step 5: Compare the Forces
Now we can compare this new force \( F \) with the original force \( F_e \):
\[ F = k \frac{Q^2}{0.16d^2} \quad \text{and} \quad F_e = k \frac{Q^2}{d^2} \]
To compare:
\[ \frac{F}{F_e} = \frac{k \frac{Q^2}{0.16d^2}}{k \frac{Q^2}{d^2}} = \frac{1}{0.16} = 6.25 \]
This means that the new force \( F \) is \( 6.25 \) times greater than the original force \( F_e \).

### Conclusion
Thus, the force of attraction between the two spheres is greater than \( F_e \).