Six charges , `q_1 = +1` `mu`C , `q_2 = +3` `mu`C , `q_3 = +4` `mu`C , `q_4 = -2` `mu`C , `q_5 = -3` `mu`C and `q_6 = -3` `mu`C are placed on a sphee of radius 10 cm. The potential at centre of sphere is

Options

A. `27xx10^5` V
B. Zero
C. `2.7xx10^5` V
D. `0.27xx10^5 V`

Answer

To find the electric potential at the center of a sphere with given charges, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Charges and Their Values**:
- \( q_1 = +1 \, \mu C \)
- \( q_2 = +3 \, \mu C \)
- \( q_3 = +4 \, \mu C \)
- \( q_4 = -2 \, \mu C \)
- \( q_5 = -3 \, \mu C \)
- \( q_6 = -3 \, \mu C \)

2. **Understand the Formula for Electric Potential**:
The electric potential \( V \) due to a point charge is given by:
\[ V = \frac{k \cdot q}{r} \]
where \( k \) is Coulomb's constant (\( k \approx 8.99 \times 10^9 \, Nm^2/C^2 \)), \( q \) is the charge, and \( r \) is the distance from the charge to the point where the potential is being calculated.

3. **Determine the Distance**:
Since all charges are placed on the surface of a sphere with a radius of 10 cm, the distance \( r \) from each charge to the center of the sphere is:
\[ r = 0.1 \, m \]

4. **Calculate the Total Potential at the Center**:
The total potential at the center \( V_{total} \) is the algebraic sum of the potentials due to each charge:
\[ V_{total} = V_1 + V_2 + V_3 + V_4 + V_5 + V_6 \]
Substituting the values:
\[ V_{total} = \frac{k \cdot q_1}{0.1} + \frac{k \cdot q_2}{0.1} + \frac{k \cdot q_3}{0.1} + \frac{k \cdot q_4}{0.1} + \frac{k \cdot q_5}{0.1} + \frac{k \cdot q_6}{0.1} \]

5. **Factor Out Common Terms**:
Since \( k \) and \( 0.1 \) are common, we can factor them out:
\[ V_{total} = \frac{k}{0.1} \left( q_1 + q_2 + q_3 + q_4 + q_5 + q_6 \right) \]

6. **Calculate the Sum of Charges**:
Now, we calculate the sum of the charges:
\[ q_{total} = 1 \, \mu C + 3 \, \mu C + 4 \, \mu C - 2 \, \mu C - 3 \, \mu C - 3 \, \mu C \]
\[ q_{total} = 1 + 3 + 4 - 2 - 3 - 3 = 0 \, \mu C \]

7. **Final Calculation of Potential**:
Substituting \( q_{total} = 0 \) into the potential equation:
\[ V_{total} = \frac{k}{0.1} \cdot 0 = 0 \, V \]

### Conclusion:
The potential at the center of the sphere is:
\[ \boxed{0 \, V} \]