QUESTION 5 b. -2q Two charges +q and -2q are placed on opposite corners of a square with side length 6 cm. The magnitude of q is 1.3 x 10 C. Calculate the magnitude of the electric field at the empty corner labeled P. (Give your answer in N/C but don't include the units.)

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### Electric Field Calculation at Vertex of a Square

#### Problem Statement

Two charges, \( +q \) and \( -2q \), are placed on opposite corners of a square with a side length of 6 cm. The charges are located at the top right and bottom left corners, respectively. The magnitude of \( q \) is \( 1.3 \times 10^{-9} \) C. Calculate the magnitude of the electric field at the empty corner labeled \( P \).

**Note:** Provide your answer in \( \text{N/C} \) but do not include the units in your response.

#### Diagram Description

The diagram provided shows a square with three points of interest:
- The top right corner is labeled with charge \( +q \).
- The bottom left corner is labeled with charge \( -2q \).
- The bottom right corner is labeled as point \( P \), where we need to calculate the electric field.

Both charges and the point \( P \) are connected with dashed lines representing the sides of the square.

#### Given Data:
- Side length of the square: 6 cm (0.06 m)
- Charge \( q \): \( 1.3 \times 10^{-9} \) C

#### Required:
- The magnitude of the electric field at point \( P \).

#### Detailed Steps to Solve the Problem:
1. **Determine the Distance:** Calculate the distance between the charges and point \( P \) in both horizontal and diagonal directions.
2. **Coulomb’s Law:** Use Coulomb's law to calculate the electric field due to each charge at point \( P \).
3. **Vector Summation:** Sum the electric fields as vectors to determine the net electric field at point \( P \).

*Note:* Ensure to convert all measurements to consistent units (SI units) before performing the calculations.
Transcribed Image Text:### Electric Field Calculation at Vertex of a Square #### Problem Statement Two charges, \( +q \) and \( -2q \), are placed on opposite corners of a square with a side length of 6 cm. The charges are located at the top right and bottom left corners, respectively. The magnitude of \( q \) is \( 1.3 \times 10^{-9} \) C. Calculate the magnitude of the electric field at the empty corner labeled \( P \). **Note:** Provide your answer in \( \text{N/C} \) but do not include the units in your response. #### Diagram Description The diagram provided shows a square with three points of interest: - The top right corner is labeled with charge \( +q \). - The bottom left corner is labeled with charge \( -2q \). - The bottom right corner is labeled as point \( P \), where we need to calculate the electric field. Both charges and the point \( P \) are connected with dashed lines representing the sides of the square. #### Given Data: - Side length of the square: 6 cm (0.06 m) - Charge \( q \): \( 1.3 \times 10^{-9} \) C #### Required: - The magnitude of the electric field at point \( P \). #### Detailed Steps to Solve the Problem: 1. **Determine the Distance:** Calculate the distance between the charges and point \( P \) in both horizontal and diagonal directions. 2. **Coulomb’s Law:** Use Coulomb's law to calculate the electric field due to each charge at point \( P \). 3. **Vector Summation:** Sum the electric fields as vectors to determine the net electric field at point \( P \). *Note:* Ensure to convert all measurements to consistent units (SI units) before performing the calculations.
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