Three point charge `q_1=1muC, q_2=-2muC` and `q_3=3muC` are placed at `(1m, 0,0), (0,2m,0)` and `(0,0,3m)` respectively. Find the electric potential at as origin.

Explanation

To find the electric potential at the origin due to the three point charges \( q_1, q_2, \) and \( q_3 \), we can use the formula for electric potential \( V \) due to a point charge, which is given by:

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

where:
- \( V \) is the electric potential,
- \( k \) is Coulomb's constant (\( 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \)),
- \( Q \) is the charge,
- \( r \) is the distance from the charge to the point where the potential is being calculated.

### Step 1: Calculate the potential due to \( q_1 \)

Given:
- \( q_1 = 1 \, \mu C = 1 \times 10^{-6} \, C \)
- Position of \( q_1 \) is at \( (1m, 0, 0) \)
- Distance from the origin \( r_1 = 1 \, m \)

Using the formula:

\[ V_1 = k \frac{q_1}{r_1} = 9 \times 10^9 \frac{1 \times 10^{-6}}{1} = 9 \times 10^3 \, V \]

### Step 2: Calculate the potential due to \( q_2 \)

Given:
- \( q_2 = -2 \, \mu C = -2 \times 10^{-6} \, C \)
- Position of \( q_2 \) is at \( (0, 2m, 0) \)
- Distance from the origin \( r_2 = 2 \, m \)

Using the formula:

\[ V_2 = k \frac{q_2}{r_2} = 9 \times 10^9 \frac{-2 \times 10^{-6}}{2} = -9 \times 10^3 \, V \]

### Step 3: Calculate the potential due to \( q_3 \)

Given:
- \( q_3 = 3 \, \mu C = 3 \times 10^{-6} \, C \)
- Position of \( q_3 \) is at \( (0, 0, 3m) \)
- Distance from the origin \( r_3 = 3 \, m \)

Using the formula:

\[ V_3 = k \frac{q_3}{r_3} = 9 \times 10^9 \frac{3 \times 10^{-6}}{3} = 9 \times 10^3 \, V \]

### Step 4: Calculate the total potential at the origin

Now, we can find the total potential \( V \) at the origin by summing the potentials due to each charge:

\[ V = V_1 + V_2 + V_3 \]

Substituting the values we calculated:

\[ V = 9 \times 10^3 + (-9 \times 10^3) + 9 \times 10^3 \]

\[ V = 9 \times 10^3 - 9 \times 10^3 + 9 \times 10^3 = 9 \times 10^3 \, V \]

### Final Answer

The electric potential at the origin is:

\[ \boxed{9000 \, V} \]