A solid metal sphere of radius 50 cm carries a charge `25xx10^-10C`. The electrostatic potential at the surface of the sphere will be

Options

A. 25 V
B. 15 V
C. 35 V
D. 45 V

Answer

To find the electrostatic potential at the surface of a solid metal sphere, we can use the formula for the potential \( V \) due to a point charge or a uniformly charged sphere, which is given by:

\[ V = \frac{k \cdot Q}{r} \]

where:
- \( V \) is the electrostatic potential,
- \( k \) is Coulomb's constant (\( 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \)),
- \( Q \) is the total charge on the sphere,
- \( r \) is the radius of the sphere.

### Step 1: Identify the given values
- Charge \( Q = 25 \times 10^{-10} \, \text{C} \)
- Radius \( r = 50 \, \text{cm} = 0.5 \, \text{m} \)

### Step 2: Substitute the values into the formula
Now, substitute the values of \( Q \) and \( r \) into the formula for \( V \):

\[ V = \frac{(8.99 \times 10^9) \cdot (25 \times 10^{-10})}{0.5} \]

### Step 3: Calculate the numerator
First, calculate the numerator:

\[ 8.99 \times 10^9 \cdot 25 \times 10^{-10} = 8.99 \times 25 \times 10^{9 - 10} = 224.75 \times 10^{-1} = 22.475 \]

### Step 4: Divide by the radius
Now, divide by the radius:

\[ V = \frac{22.475}{0.5} = 44.95 \, \text{V} \]

### Final Answer
The electrostatic potential at the surface of the sphere is approximately:

\[ V \approx 44.95 \, \text{V} \]

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