A non conducting spherical shell of diameter 10 cm has a charge of `1.6 xx 10^(-4)C`. A charge of 20 C is placed at a distance of 10 cm from its centre, then force between them will be :-

Options

A. `4 xx 10^(9)N`
B. `16 xx 10^(15)N`
C. `3 xx 10^(9)N`
D. `6 xx 10^(-9) N`

Answer

To find the force between a non-conducting spherical shell and a point charge, we can follow these steps:

### Step 1: Identify the given values
- Diameter of the spherical shell = 10 cm
- Charge on the spherical shell, \( Q = 1.6 \times 10^{-4} \, C \)
- Charge placed at a distance from the center, \( q = 20 \, C \)
- Distance from the center of the shell to the point charge = 10 cm

### Step 2: Calculate the radius of the spherical shell
The radius \( r \) of the spherical shell is half of the diameter:
\[ r = \frac{10 \, \text{cm}}{2} = 5 \, \text{cm} = 0.05 \, \text{m} \]

### Step 3: Determine the distance from the center of the shell to the point charge
The distance from the center of the shell to the point charge is given as:
\[ R = 10 \, \text{cm} = 0.1 \, \text{m} \]

### Step 4: Calculate the electric field due to the spherical shell at the location of the point charge
For a non-conducting spherical shell, the electric field outside the shell (at a distance greater than the radius) is given by:
\[ E = \frac{kQ}{R^2} \]
where \( k = \frac{1}{4\pi \epsilon_0} \approx 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \).

Substituting the values:
\[ E = \frac{(9 \times 10^9) \times (1.6 \times 10^{-4})}{(0.1)^2} \]
\[ E = \frac{(9 \times 10^9) \times (1.6 \times 10^{-4})}{0.01} \]
\[ E = (9 \times 10^9) \times (1.6 \times 10^{-4}) \times 100 \]
\[ E = (9 \times 1.6) \times 10^9 \times 10^{-2} \]
\[ E = 14.4 \times 10^7 \, \text{N/C} \]

### Step 5: Calculate the force on the point charge due to the electric field
The force \( F \) on the point charge \( q \) due to the electric field \( E \) is given by:
\[ F = qE \]
Substituting the values:
\[ F = 20 \times (14.4 \times 10^7) \]
\[ F = 288 \times 10^7 \, \text{N} \]
\[ F = 2.88 \times 10^9 \, \text{N} \]

### Step 6: Conclusion
The force between the non-conducting spherical shell and the point charge is approximately:
\[ F \approx 3 \times 10^9 \, \text{N} \]