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The differential equation of all non-horizontal lines in a plane is :

Maths-General

  1. fraction numerator d y over denominator d x end fraction equals 0
  2. fraction numerator d x over denominator d y end fraction equals 0
  3. fraction numerator d squared y over denominator d x squared end fraction equals 0
  4. fraction numerator d squared x over denominator d y squared end fraction equals 0

    Answer:The correct answer is: fraction numerator d squared x over denominator d y squared end fraction equals 0

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    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

    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

    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

    physics-General
    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
    General
    physics-

    A hollow conducting sphere is placed in an electric field produced by a point charge placed at P as shown in figure. V subscript A end subscript comma blank V subscript B end subscript comma blank V subscript c end subscriptbe the potentials at points A, B and C respectively. Then

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    So, V subscript A end subscript equals V subscript B end subscript equals V subscript C end subscript

    A hollow conducting sphere is placed in an electric field produced by a point charge placed at P as shown in figure. V subscript A end subscript comma blank V subscript B end subscript comma blank V subscript c end subscriptbe the potentials at points A, B and C respectively. Then

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    At each point on the surface of a conducting sphere the potential is equal.
    So, V subscript A end subscript equals V subscript B end subscript equals V subscript C end subscript