The electric field at P has x -component and y-component. – [Free] B53
The electric field at P has x -component and y-component
![The electric field at P has x -component and y-component. - [Free] B53](data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20640%20480'%3E%3C/svg%3E)
Answer
Electric Field Components at Point P
🔹 Step 1: Identifying the Configuration
Two identical point charges of magnitude Q are located symmetrically at (+a, 0) and (−a, 0) on the x-axis. Point P lies on the y-axis at (0, b).
This symmetrical setup simplifies component calculations due to mirrored geometry.
🔹 Step 2: Calculating Distance to Point P
The distance from each charge to point P is calculated using the Pythagorean theorem:
r = √(a² + b²)
🔹 Step 3: Electric Field Magnitude from One Charge
Using Coulomb’s Law, the electric field due to a single point charge:
E = kQ / r²
Where:
k= Coulomb’s constantQ= magnitude of the point charger= distance from the charge to point P
🔹 Step 4: Resolving into Components
Due to symmetry:
- X-components cancel out (equal in magnitude, opposite in direction).
- Y-components add up. Each is given by:
Ey = (kQ / r²) × (b / r) = kQb / r³
Total y-component from both charges:
Ey = 2 × (kQb / r³)
🔹 Step 5: Final Electric Field Components at P
Using r = √(a² + b²), the final components are:
Ex = 0
Ey = 2kQb / (a² + b²)3/2
✅ Final Result
Electric field vector at P:
(Ex, Ey) = (0, 2kQb / (a² + b²)3/2)
(Ex, Ey) = (0, 2kQb / (a² + b²)3/2)