Show that potential difference can be described as energy transferred per unit charge between the two points.

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Show that potential difference can be described as energy transferred per unit charge between the two points.

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Minh Khuê 4 years 2021-08-02T07:40:46+00:00 1 Answers 104 views 0

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  1. ThanhThu
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    2021-08-02T07:42:14+00:00
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    Answer:

    The potential difference, ΔV, between two points in the electric field can be described as the potential energy transferred per unit charge, ΔU/q₀ , between the two points

    ΔV = ΔU/q₀

    Explanation:

    The force, F, acting on a test charge, q₀, placed in an electric field E is given as follows;

    F = q₀·E

    The work the electric field does on the charge, W =dU =  F·ds = q₀·E”·dS

    \Delta U = q_0 \times \int\limits^B_A {E \cdot } \, ds

    The electric potential difference, ΔV, between two points in the electric which is the change in the energy of the system when a test charge is moved between points in the field is goven as follows;

    \Delta V = \dfrac{\Delta U}{q_0} = -\int\limits^B_A {E \cdot } \, ds

    Therefore, given that, we have;

    \Delta V = \dfrac{\Delta U}{q_0} = \dfrac{-q_o \times \int\limits^B_A {E \cdot } \, ds}{q_0} = \dfrac{F \cdot ds}{q_0} = \dfrac{W}{q_0}

    Therefore, the potential energy transferred per unit charge, ΔU/q₀ can be described as the potential difference between two points in the electric field, and vice versa.

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