JEE Main202124 Feb 2021Morning ShiftPhysicsElectrostaticsActual
A cube of side a has point charges + Q located at each of its vertices except at the origin where the charge is - Q . The electric field at the centre of cube is:
Options
- A- Q 3 3 π ε 0 a 2 x ^ + y ^ + z ^
- BQ 3 3 π ε 0 a 2 x ^ + y ^ + z ^
- C- 2 Q 3 3 π ε 0 a 2 x ^ + y ^ + z ^
- D2 Q 3 3 π ε 0 a 2 x ^ + y ^ + z ^
Correct answer
C. - 2 Q 3 3 π ε 0 a 2 x ^ + y ^ + z ^
Step-by-step solution
We can replace - Q charge at origin by + Q and - 2 Q . Now due to + Q charge at every corner of cube. Electric field at center of cube is zero so now net electric field at center is only due to - 2 Q charge at origin. E → = k q r → r 3 = 1 - 2 Q a 2 x ^ + y ^ + z ^ 4 π ε 0 a 2 3 3 E → = - 2 Q x ^ + y ^ + z ^ 3 3 π a 2 ε 0