At what position or positions on the x-axis is the electric field zero?

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At what position or positions on the x-axis is the electric field zero?

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Eirian 3 years 2021-08-25T01:53:19+00:00 1 Answers 20 views 0

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    2021-08-25T01:54:23+00:00

    Answer:

    The electric field will be zero at x = ± ∞.

    Explanation:

    Suppose, A -2.0 nC charge and a +2.0 nC charge are located on the x-axis at x = -1.0 cm and x = +1.0 cm respectively.

    We know that,

    The electric field is

    E=\dfrac{kq}{r^2}

    The electric field vector due to charge one

    \vec{E_{1}}=\dfrac{kq_{1}}{r_{1}^2}(\hat{x})

    The electric field vector due to charge second

    \vec{E_{2}}=\dfrac{kq_{2}}{r_{2}^2}(-\hat{x})

    We need to calculate the electric field

    Using formula of net electric field

    \vec{E}=\vec{E_{1}}+\vec{E_{2}}

    \vec{E_{1}}+\vec{E_{2}}=0

    Put the value into the formula

    \dfrac{kq_{1}}{r_{1}^2}(\hat{x})+\dfrac{kq_{2}}{r_{2}^2}(-\hat{x})=0

    \dfrac{kq_{1}}{r_{1}^2}(\hat{x})=\dfrac{kq_{2}}{r_{2}^2}(\hat{x})

    (\dfrac{r_{2}}{r_{1}})^2=\dfrac{q_{2}}{q_{1}}

    \dfrac{r_{2}}{r_{1}}=\sqrt{\dfrac{q_{2}}{q_{1}}}

    Put the value into the formula

    \dfrac{2.0+x}{x}=\pm\sqrt{\dfrac{2.0}{2.0}}

    2.0+x=x

    If x = ∞, then the equation is be satisfied.

    Hence, The electric field will be zero at x = ± ∞.

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )