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 elect

Question

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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Eva 4 weeks 2021-12-26T11:29:48+00:00 1 Answer 0 views 0

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    2021-12-26T11:30:54+00:00

    Answer:

    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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