Physics-
General
Easy

Question

The figure shows electric potential V as a function of x. Rank the four regions according to the magnitude of x-component of the electric field E within them, greatest first

  1. E subscript 4 end subscript greater than E subscript 2 end subscript greater than E subscript 3 end subscript greater than E subscript 1 end subscript    
  2. E subscript 2 end subscript greater than E subscript 4 end subscript greater than E subscript 1 end subscript equals E subscript 3 end subscript    
  3. E subscript 1 end subscript greater than E subscript 2 end subscript greater than E subscript 3 end subscript greater than E subscript 4 end subscript    
  4. E subscript 1 end subscript greater than E subscript 3 end subscript greater than E subscript 2 end subscript greater than E subscript 4 end subscript    

The correct answer is: E subscript 2 end subscript greater than E subscript 4 end subscript greater than E subscript 1 end subscript equals E subscript 3 end subscript


    Electric field
    E equals negative fraction numerator d V over denominator d x end fraction
    For I region, V subscript 1 end subscript=constant

    therefore blank fraction numerator d V subscript 1 end subscript over denominator d x end fraction equals 0 blank
    therefore blank E subscript 1 end subscript equals 0 blank
    For II region,
    V subscript 2 end subscript equals plus v e equals plus f open parentheses x close parentheses
    therefore E subscript 2 end subscript equals negative fraction numerator d V subscript 2 end subscript over denominator d x end fraction equals negative v e
    For III region.
    V subscript 3 end subscript=constant
    therefore blank fraction numerator d V subscript 3 end subscript over denominator d x end fraction equals 0 blank
    therefore blank E subscript 3 end subscript equals 0 blank
    For IV region, V subscript 1 end subscript equals negative f open parentheses x close parentheses
    therefore blank E subscript 4 end subscript equals negative fraction numerator d V subscript 4 end subscript over denominator d x end fraction equals plus v e
    From these values, we have
    E subscript 2 end subscript greater than E subscript 4 end subscript greater than E subscript 1 end subscript equals E subscript 3 end subscript

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