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The electric field in a region is given byopen parentheses straight E with rightwards arrow on top equals 3 over 5 straight E subscript 0 straight i with not stretchy hat on top plus 4 over 5 straight E subscript 0 straight j with not stretchy hat on top close parentheses N over C. The ratio of flux of reported field through the rectangular surface of area 0.2 m2 (parallel to y-z plane) to that of the surface of area 0.3 m2 (parallel to x-z plane) is a: b, where a = ________

  1. 1 half
  2. 1 third
  3. 1 fourth
  4. 1 fifth

The correct answer is: 1 half


    text  Given : Electric field,  end text E with not stretchy rightwards arrow on top equals 3 over 5 E subscript 0 i with not stretchy hat on top plus 4 over 5 E subscript 0 j with not stretchy hat on top N over C
text  Area (Parallel to  end text y minus z text  plane),  end text A subscript a equals 0.2 i with not stretchy hat on top straight m squared
text  Area (Parallel to  end text straight x minus straight z text  plane),  end text straight A subscript straight b equals 0.3 straight j with not stretchy hat on top straight m squared
text  Flux,  end text straight ϕ subscript straight a equals straight E with not stretchy rightwards arrow on top times straight A with not stretchy rightwards arrow on top subscript straight a equals open parentheses 3 over 5 straight E subscript 0 straight i with not stretchy hat on top plus 4 over 5 straight E subscript 0 straight j with not stretchy hat on top close parentheses times 0.2 straight i with not stretchy hat on top equals 6 over 50 straight E subscript 0
straight ϕ subscript straight b equals straight E with not stretchy rightwards arrow on top times straight A with not stretchy rightwards arrow on top subscript straight b equals open parentheses 3 over 5 straight E subscript 0 straight i with not stretchy hat on top plus 4 over 5 straight E subscript 0 straight j with not stretchy hat on top close parentheses times 0.3 straight j with not stretchy hat on top equals 12 over 50 straight E subscript 0
therefore straight ϕ subscript straight a over straight ϕ subscript straight b equals fraction numerator 6 divided by 50 straight E subscript 0 over denominator 12 divided by 50 straight E subscript 0 end fraction equals 1 half

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