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The question in the image is about calculating the magnitude of a third charge that will make the electric field at a certain point zero.

**Translation and Problem Overview:**
Two point charges are positioned on the x-axis:
- \( Q_1 = 2.5 \, \text{pC} \) at \( x = -10 \, \text{cm} \),
- \( Q_2 = 5 \, \text{pC} \) at \( x = 0 \, \text{cm} \).

We want to place a third charge at \( x = +20 \, \text{cm} \) such that the net electric field at \( x = +10 \, \text{cm} \) becomes zero. The goal is to calculate the magnitude of the third charge.

### Steps to Solve:
1. **Electric Field Formula**: The electric field due to a point charge \( Q \) at a distance \( r \) is given by:
   \[
   E = \frac{k Q}{r^2}
   \]
   where \( k \) is Coulomb's constant, \( k = 9 \times 10^9 \, \text{Nm}^2/\text{C}^2 \).

2. **Superposition Principle**: The total electric field at \( x = +10 \, \text{cm} \) is the sum of the fields due to \( Q_1 \), \( Q_2 \), and the third charge \( Q_3 \). For the electric field to be zero, the sum of these fields must equal zero.

3. **Positions**:
   - The distance between \( x = +10 \, \text{cm} \) and \( Q_1 \) at \( x = -10 \, \text{cm} \) is \( r_1 = 20 \, \text{cm} \).
   - The distance between \( x = +10 \, \text{cm} \) and \( Q_2 \) at \( x = 0 \, \text{cm} \) is \( r_2 = 10 \, \text{cm} \).
   - The distance between \( x = +10 \, \text{cm} \) and \( Q_3 \) at \( x = +20 \, \text{cm} \) is \( r_3 = 10 \, \text{cm} \).

4. **Setting up the equation**: Using the condition that the net electric field at \( x = +10 \, \text{cm} \) is zero, we can express the electric field contributions from each charge and set up the equation.

I will calculate the required third charge \( Q_3 \).The magnitude of the third charge \( Q_3 \) needed to make the electric field zero at \( x = +10 \, \text{cm} \) is \( 5.625 \, \text{pC} \). 

Since the result is negative, it means that the third charge should be negative to counterbalance the fields from the positive charges \( Q_1 \) and \( Q_2 \).

### Do you want further clarification or details about any step?

Here are 5 related questions you might consider:
1. How does the sign of a charge affect the direction of the electric field it produces?
2. How do you apply the superposition principle to other electric field problems?
3. What are the effects of placing charges closer or farther from the point of interest?
4. Can we solve similar problems with charges arranged in different shapes, like a triangle?
5. How does the electric potential differ from the electric field in such configurations?

**Tip**: Remember, the electric field vector points away from positive charges and towards negative charges!

Two point charges are positioned on the x-axis. Q1 = 2.5 pC at x = -10 cm and Q2 = 5 pC at x = 0 cm. We want to place a third charge at x = +20 cm such that the electric field at x = +10 cm becomes zero. Calculate the magnitude of the third charge.

This problem involves calculating the magnitude of a third charge that will make the electric field zero at a certain point on the x-axis, considering two known charges. The solution involves applying Coulomb's law and the superposition principle.

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