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Electric field from potential given as a function of x, or the reverse

This type of question, asked 3 times: May 2021 S1, 10 May 2024 S2, 19 Apr 2025 S2. All 3 questions below, oldest first.

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  1. Question 1

    May 2021 S1

    33
    The potential at a point xx (measured in μ\mum) due to some charges situated on the X-axis is given by V(x)=20x2−4 VV(x) = \frac{20}{x^2-4}\ \text{V}. The electric field EE at x=4 μmx = 4\ \mu\text{m} is given by

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  2. Question 2

    10 May 2024 S2

    32
    Assume that an electric field E⃗=30x2 i^\vec{E}=30x^2\,\hat{i} exists in space. If 'V0V_0' is the potential at the origin and 'VAV_A' is the potential at x=2 mx=2\,m, then the potential difference VA−V0V_A - V_0 is

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  3. Question 3

    19 Apr 2025 S2

    10
    The electric potential ' VV ' is given as a function of distance ' xx ' (metre) by V=(4x2+8x−3)VV=\left( 4x^{2}+ 8x- 3 \right)V. The value of electric field at x=0.5 mx= 0.5\text{ }m, in V/mV/m is

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