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The relationship between the electric field and the rate of change of potential at a specific location is expressed as follows:

1. E = -dV/dr
2. E = -dV/dx î + dV/dy ĵ + dV/dz k̂
3. E = [(2xy + z³) î + ĵ + 2x² k̂ + 3xz²]
4. None of the above

Correct answer: E = -dV/dr

Solution

The electric field is defined as the negative gradient of the electric potential, which is mathematically expressed as E = -∂V/∂r. This is a fundamental concept in electrostatics.

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