Point charges each of magnitude Q are placed at three corners of a square . What is the direction of the resultant electric field at the fourth corner ?

Options

A. OC
B. OE
C. OD
D. OB

Answer

To solve the problem of finding the direction of the resultant electric field at the fourth corner of a square where three corners have point charges of magnitude Q, we can follow these steps:

### Step 1: Understand the Configuration
We have a square with point charges of magnitude Q placed at three corners. Let's label the corners of the square as A, B, C, and D. Assume charges are placed at corners A, B, and C, while corner D is the one where we need to find the resultant electric field.

### Step 2: Determine the Electric Field Due to Each Charge
1. **Electric Field at Corner D due to Charge at A (E_A)**:
- The electric field due to a positive charge points away from the charge. Therefore, the electric field at D due to charge at A will point directly away from A towards D.

2. **Electric Field at Corner D due to Charge at B (E_B)**:
- Similarly, the electric field at D due to charge at B will also point away from B towards D.

3. **Electric Field at Corner D due to Charge at C (E_C)**:
- The electric field at D due to charge at C will point away from C towards D.

### Step 3: Analyze the Directions of the Electric Fields
- The electric field E_A will point horizontally towards the right (if A is at the top left corner).
- The electric field E_B will point vertically downwards (if B is at the top right corner).
- The electric field E_C will point diagonally towards D from C (which is at the bottom right corner).

### Step 4: Vector Addition of Electric Fields
- The electric fields E_A and E_B are perpendicular to each other.
- The resultant electric field due to E_A and E_B can be found using the Pythagorean theorem since they are at right angles to each other.
- The resultant vector will point diagonally from the origin of E_A and E_B, which is towards the bottom right corner of the square.

### Step 5: Conclusion
The direction of the resultant electric field at corner D will be along the diagonal of the square, pointing towards the bottom right corner of the square.

### Final Answer
The direction of the resultant electric field at the fourth corner (D) is diagonally towards the bottom right corner of the square.

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