To solve Part (b), where you are asked to find the electric field halfway between the two charges, we need to apply the formula for the electric field created by a point charge, which is given by:

$E = \frac{k \cdot |q|}{r^2}$

Where:

• $E$ is the electric field (in newtons per coulomb, N/C),
• $k$ is Coulomb's constant, $k = 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2$,
• $q$ is the charge (in coulombs),
• $r$ is the distance from the charge (in meters).

Step-by-step approach:

1. Distance from each charge to the halfway point: The charges are 0.25 m apart, so halfway between them is at $r = \frac{0.25}{2} = 0.125 \, \text{m}$.

2. Calculate the electric field due to each charge at this halfway point using the formula $E = \frac{k \cdot |q|}{r^2}$.

   • For the $0.22 \, \mu \text{C}$ charge: $E_1 = \frac{8.99 \times 10^9 \times 0.22 \times 10^{-6}}{(0.125)^2}$

   • For the $0.76 \, \mu \text{C}$ charge: $E_2 = \frac{8.99 \times 10^9 \times 0.76 \times 10^{-6}}{(0.125)^2}$

3. Combine the electric fields: Since both charges are positive, the electric fields will point away from each charge. Thus, they will reinforce each other in the region between the two charges.

Let me calculate this for you.The total electric field halfway between the two charges is approximately $563,853 \, \text{N/C}$.

Would you like further details or have any additional questions?

Here are some related questions to consider:

1. How does the electric field behave near a positive versus a negative charge?
2. How would the electric field change if the charges were different signs?
3. What is the superposition principle in relation to electric fields?
4. How does the distance between charges affect the magnitude of the electric field?
5. How do you determine the direction of the electric field at any given point?

Tip: Remember that electric fields from like charges reinforce each other when calculated at points between them but oppose each other if the charges are of opposite signs.