The diameter of a hollow metallic sphere is 60 cm and the sphere carries a charge of `500 muC`. The potential at a distance of `100 cm` from the centre of the sphere will be

Options

A. `6 xx 10^(7)V`
B. `7 xx 10^(6)V`
C. `4.5 xx 10^(6)V`
D. `5 xx 10^(6)V`

Answer

To find the potential at a distance of 100 cm from the center of a hollow metallic sphere with a charge of 500 µC, we can follow these steps:

### Step 1: Identify the given values
- Diameter of the sphere = 60 cm
- Radius of the sphere (R) = Diameter / 2 = 60 cm / 2 = 30 cm = 0.3 m
- Charge (Q) = 500 µC = 500 × 10^-6 C = 5 × 10^-4 C
- Distance from the center (r) = 100 cm = 1 m

### Step 2: Use the formula for electric potential
The electric potential (V) at a distance r from the center of a charged sphere is given by the formula:
\[ V = \frac{k \cdot Q}{r} \]
where:
- \( k \) is Coulomb's constant, approximately \( 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \)
- \( Q \) is the charge
- \( r \) is the distance from the center of the sphere

### Step 3: Substitute the values into the formula
Substituting the values into the formula:
\[ V = \frac{8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \cdot 5 \times 10^{-4} \, \text{C}}{1 \, \text{m}} \]

### Step 4: Calculate the potential
Now, perform the calculation:
\[ V = 8.99 \times 10^9 \cdot 5 \times 10^{-4} \]
\[ V = 44.95 \times 10^6 \]
\[ V = 4.495 \times 10^7 \, \text{V} \]

### Step 5: Round the result
The potential can be rounded to:
\[ V \approx 4.5 \times 10^6 \, \text{V} \]

### Conclusion
Thus, the potential at a distance of 100 cm from the center of the sphere is approximately \( 4.5 \times 10^6 \, \text{V} \).