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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

  1. A- Q 3 3 π ε 0 a 2 x ^ + y ^ + z ^
  2. BQ 3 3 π ε 0 a 2 x ^ + y ^ + z ^
  3. C- 2 Q 3 3 π ε 0 a 2 x ^ + y ^ + z ^
  4. 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

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