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Over a certain region of space, the electric potential is V = 4x - 7x2y + 7yz2. Find the expressions for the x, y, z components of the electric field over this region. (Use any variable or symbol stated above as necessary.)

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  1. 8 April, 05:40
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    Ex = - 4 + 14xy

    Ey = 7x² - 7z²

    Ez = - 14yz

    Step-by-step explanation:

    The relationship between Electric field Er (x, y, z) and Electric potential, V, is a differential relationship:

    Er (x, y, z) = - dV/dr (x, y, z)

    Where r (x, y, z) = distance in x, y and z components.

    The x component of the electric field is:

    Ex = - dV/dx

    Given that:

    V = 4x - 7x²y + 7yz²

    Ex = - dV/dx

    Ex = - (4 - 14xy)

    Ex = - 4 + 14xy

    The y component of the electric field is:

    Ey = - dV/dy

    Ey = - (-7x² + 7yz²)

    Ey = 7x² - 7z²

    The z component of the electric field is:

    Ez = - dV/dz

    Ez = - (14yz)

    Ez = - 14yz
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