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Question

Four charges are placed on corners of a square as shown in figure having side of 5 c m. If Q is one microcoulomb, then electric field intensity at centre will be

  1. 1.02 cross times 1 0 to the power of 7 end exponent N divided by C upwards    
  2. 2.04 cross times 1 0 to the power of 7 end exponent N divided by C downwards    
  3. 2.04 cross times 1 0 to the power of 7 end exponent N divided by C upwards    
  4. 1.02 cross times 1 0 to the power of 7 end exponent N divided by C downwards    

The correct answer is: 1.02 cross times 1 0 to the power of 7 end exponent N divided by C upwards


    Side a = 5 ´ 10–2 m
    Half of the diagonal of the square r equals fraction numerator a over denominator square root of 2 end fraction
    Electric field at centre due to charge q E equals fraction numerator k q over denominator open parentheses fraction numerator a over denominator square root of 2 end fraction close parentheses to the power of 2 end exponent end fraction

    Now field at O equals square root of E to the power of 2 end exponent plus E to the power of 2 end exponent end root equals E square root of 2 equals fraction numerator k q over denominator open parentheses fraction numerator a over denominator square root of 2 end fraction close parentheses to the power of 2 end exponent end fraction. square root of 2
    equals fraction numerator 9 cross times 1 0 to the power of 9 end exponent cross times 1 0 to the power of negative 6 end exponent cross times square root of 2 cross times 2 over denominator left parenthesis 5 cross times 1 0 to the power of negative 2 end exponent right parenthesis to the power of 2 end exponent end fraction equals 1.02 cross times 1 0 to the power of 7 end exponent N divided by C (upward)

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