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• October 11, 2021

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• PHY102 Physics II © Dr.Cem Özdoğan

• 24-10 Calculating the Field from the Potential

• Suppose that a positive test charge q0 moves through a displacement from one equipotential surface to the adjacent surface.
• The work the electric field does on the test charge during the move is -q0 dV.
• The work done by the electric field may also be written as the scalar product of
• =q0E(cosθ)ds.

• Therefore, the component of E in any direction is the negative of the rate at which the electric potential changes with distance in that direction.

• If we take the s axis to be, in turn, the x, y, and z axes, the x, y, and z components of E at any point are

• ΔU=q0ΔV=-W

• FΔs=q0EΔs=W

• Therefore,
• That is,

• Since E cos θ is the component of E in the direction of ds,