JEE Main202228 Jun 2022Morning ShiftPhysicsElectrostaticsActual
The three charges q 2 , q and q 2 are placed at the corners A , D and C of a square of side a as shown in figure. The magnitude of electric field E at the corner B of the square, is
Options
- Aq 4 π ϵ 0 a 2 1 2 + 1 2
- Bq 4 π ϵ 0 a 2 1 + 1 2
- Cq 4 π ϵ 0 a 2 1 - 1 2
- Dq 4 π ϵ 0 a 2 1 2 - 1 2
Correct answer
A. q 4 π ϵ 0 a 2 1 2 + 1 2
Step-by-step solution
E A = k q 2 a 2 = k q 2 a 2 , E C = k q 2 a 2 = k q 2 a 2 and E D = k q 2 a 2 = k q 2 a 2 As we can see from diagram, E C   &   E A are perpendicular. Therefore, net electric field will be, = k q 2 a 2 + k q 2 a 2 2 + k q 2 a 2 2 = k q 2 a 2 + k q 2 a 2 = q 4 π ϵ 0 a 2 1 2 + 1 2