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For a uniform electric field ⃗E = E₀ ̂i, if the electric potential at x = 0 is zero, then the value of the electric potential at a distance x along the +x direction will be _______.

Asked in GSEB Board July 2016 · Relation between field and potential

• (1) -xE₀
• (2) xE₀
• (3) x²E₀
• (4) -x²E₀

Step-by-step solution

Why the other options are wrong

• (2) Sign slip: the potential falls along the direction of the field, so moving a distance x along +̂i lowers V by E₀x. A value of +xE₀ would mean the potential rises along the field.
• (3) Not an arithmetic slip but a units error: E₀ is in V m⁻¹, so x²E₀ is in V m, not volts. In a uniform field the potential changes linearly with x.
• (4) Right sign, wrong power of x: x²E₀ is in V m, so it cannot be a potential. A uniform field gives a linear fall, -E₀x.

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