To find the net electric field at point [tex]\(P\)[/tex] due to the two charges [tex]\(Q_1\)[/tex] and [tex]\(Q_2\)[/tex], we will follow these steps:
1. Identify the electric field due to each charge at point [tex]\(P\)[/tex]:
- The electric field at [tex]\(P\)[/tex] due to [tex]\(Q_1\)[/tex] is given as [tex]\(E_{Q1} = 1.5 \times 10^5\)[/tex] newtons/coulomb.
- The electric field at [tex]\(P\)[/tex] due to [tex]\(Q_2\)[/tex] is given as [tex]\(E_{Q2} = 7.2 \times 10^5\)[/tex] newtons/coulomb.
2. Determine the direction of the electric fields:
- Assume that the fields due to [tex]\(Q_1\)[/tex] and [tex]\(Q_2\)[/tex] are along the same line but in opposite directions since [tex]\(P\)[/tex] is exactly between the two charges.
3. Calculate the net electric field at point [tex]\(P\)[/tex]:
- Subtract the smaller electric field magnitude from the larger one to find the net electric field.
[tex]\[
E_{\text{net}} = E_{Q2} - E_{Q1}
\][/tex]
4. Substitute the given values:
[tex]\[
E_{\text{net}} = 7.2 \times 10^5 \, \text{N/C} - 1.5 \times 10^5 \, \text{N/C}
\][/tex]
5. Compute the result:
[tex]\[
E_{\text{net}} = 5.7 \times 10^5 \, \text{N/C}
\][/tex]
Therefore, the net electric field at point [tex]\(P\)[/tex] is [tex]\(5.7 \times 10^5\)[/tex] newtons/coulomb.
The correct answer is:
C. [tex]\( 5.7 \times 10^5 \)[/tex] newtons/coulomb
