in the diagram, $q_1 = +6.60\times10^{-9} c$ and $q_2 = +3.10\times10^{-9} c$. find the magnitude of the…

Explanation:

Step1: Calculate the electric field magnitude due to charge $q_1$ at point P.

The electric field $E_1$ due to $q_1$ at point P is given by Coulomb's law: $E_1 = k \frac{|q_1|}{r_1^2}$, where $k = 8.99 \times 10^9 , \text{N} \cdot \text{m}^2/\text{C}^2$, $q_1 = +6.60 \times 10^{-9}$ C, and $r_1 = 0.350$ m. Since $q_1$ is positive, $E_1$ points away from $q_1$ (to the right). $$ E_1 = (8.99 \times 10^9 , \text{N} \cdot \text{m}^2/\text{C}^2) \frac{6.60 \times 10^{-9} , \text{C}}{(0.350 , \text{m})^2} $$ $$ E_1 = (8.99 \times 10^9) \frac{6.60 \times 10^{-9}}{0.1225} , \text{N/C} $$ $$ E_1 \approx 484.36 , \text{N/C} $$

Step2: Calculate the electric field magnitude due to charge $q_2$ at point P.

The electric field $E_2$ due to $q_2$ at point P is given by Coulomb's law: $E_2 = k \frac{|q_2|}{r_2^2}$, where $q_2 = +3.10 \times 10^{-9}$ C, and $r_2 = 0.155$ m. Since $q_2$ is positive, $E_2$ points away from $q_2$ (upwards). $$ E_2 = (8.99 \times 10^9 , \text{N} \cdot \text{m}^2/\text{C}^2) \frac{3.10 \times 10^{-9} , \text{C}}{(0.155 , \text{m})^2} $$ $$ E_2 = (8.99 \times 10^9) \frac{3.10 \times 10^{-9}}{0.024025} , \text{N/C} $$ $$ E_2 \approx 1159.99 , \text{N/C} $$

Step3: Calculate the magnitude of the total electric field at point P.

The total electric field $E_{total}$ at P is the vector sum of $E_1$ and $E_2$. Since $E_1$ points to the right and $E_2$ points upwards, they are perpendicular. The magnitude of the total electric field is found using the Pythagorean theorem. $$ |E_{total}| = \sqrt{E_1^2 + E_2^2} $$ $$ |E_{total}| = \sqrt{(484.36 , \text{N/C})^2 + (1159.99 , \text{N/C})^2} $$ $$ |E_{total}| = \sqrt{234604.6 + 1345576.8} , \text{N/C} $$ $$ |E_{total}| = \sqrt{1580181.4} , \text{N/C} $$ $$ |E_{total}| \approx 1257.05 , \text{N/C} $$

Step4: Round the final answer to the correct number of significant figures.

The given values have three significant figures. Therefore, the final answer should be rounded to three significant figures. $$ |E_{total}| \approx 1260 , \text{N/C} $$

Answer:

1260