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Flux or enclosed charge for a cube or cuboid in a field that varies with position

This type of question, asked 5 times: 2021 Paper 24, 30 Jan 2023, 31 Jan 2023, 1 Feb 2023, 9 Apr 2024. All 5 questions below, oldest first.

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  1. Question 1

    2021 Paper 24

    1
    A cube is placed inside an electric field, E→=150y2j^\overrightarrow{E}= 150y^{2}\widehat{j}. The side of the cube is 0.5 m0.5\text{ }m and is placed in the field as shown in the given figure. The charge inside the cube is:

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  2. Question 2

    30 Jan 2023

    118
    As shown in figure, a cuboid lies in a region with electric field E→=2x2ı^−4yȷ^+6k^ N/C\overrightarrow{E} = 2x^{2}\widehat{\imath}- 4y\widehat{\jmath}+ 6\widehat{k}\text{ }N/C. The magnitude of charge within the cuboid is n∈0Cn\in_{0}C. The value of n_____n\_\_\_\_\_ is (if dimension of cuboid is 1×2×3 m31 \times 2 \times 3{\text{ }m}^{3} ).

  3. Question 3

    31 Jan 2023

    29
    Expression for an electric field is given by E→=4000x2ı^Vm\overrightarrow{E}= 4000x^{2}\widehat{\imath}\frac{V}{m}. The electric flux through the cube of side 20 cm20\text{ }cm when placed in electric field (as shown in the figure) is______ VV cm

  4. Question 4

    1 Feb 2023

    116
    A cubical volume is bounded by the surfaces x=0,x=a,y=0,y=a,z=0,z=ax = 0,x = a,y = 0,y = a,z = 0,z = a. The electric field in the region is given by E→=E0xı^\overrightarrow{E}=E_{0}x\widehat{\imath}. Where E0=4×104NC−1 m−1E_{0}= 4 \times10^{4}NC^{- 1}{\text{ }m}^{- 1}. If a=2 cma = 2\text{ }cm, the charge contained in the cubical volume is Q×10−14CQ \times10^{- 14}C. The value of QQ is .___ (Take  ϵ0=9×10−12C2Nm2)\left. \ \epsilon_{0}= 9 \times\frac{10^{- 12}C^{2}}{Nm^{2}} \right)

  5. Question 5

    9 Apr 2024

    114
    An electric field E→=(2xi^)NC−1\overrightarrow{E}= (2x\widehat{i})NC^{- 1} exists in space. AA cube of side 2 m2\text{ }m is placed in the space as per figure given below. The electric flux through the cube is________ Nm2/CNm^{2}/C.