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 electric 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 data
- Diameter of the hollow metallic sphere = 60 cm
- Charge on the sphere, \( Q = 500 \, \mu C = 500 \times 10^{-6} \, C \)
- Distance from the center, \( r = 100 \, cm = 1 \, m \)

### Step 2: Calculate the radius of the sphere
The radius \( R \) of the sphere is half of the diameter:
\[ R = \frac{60 \, cm}{2} = 30 \, cm = 0.3 \, m \]

### Step 3: Determine the position of the point
Since the distance \( r = 1 \, m \) is greater than the radius \( R = 0.3 \, m \), the point is outside the sphere.

### Step 4: Use the formula for electric potential outside a charged sphere
For a point outside a charged sphere, the electric potential \( V \) is given by:
\[ V = \frac{kQ}{r} \]
where \( k \) is Coulomb's constant, \( k \approx 9 \times 10^9 \, N \cdot m^2/C^2 \).

### Step 5: Substitute the values into the formula
Substituting the values into the formula:
\[ V = \frac{(9 \times 10^9) \times (500 \times 10^{-6})}{1} \]

### Step 6: Calculate the potential
Calculating the potential:
\[ V = \frac{(9 \times 10^9) \times (500 \times 10^{-6})}{1} = 9 \times 10^9 \times 500 \times 10^{-6} \]
\[ V = 9 \times 500 \times 10^3 = 4500 \, V \]

### Step 7: Final answer
Thus, the potential at a distance of 100 cm from the center of the sphere is:
\[ V = 4500 \, V \]