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The unit of the physical quantity obtained by the line integral of the electric field is ______.

Asked in GUJCET 2011 · Relation between field and potential

• (1) N C⁻¹
• (2) V m⁻¹
• (3) J C⁻¹
• (4) C² N⁻¹ m⁻²

Step-by-step solution

Why the other options are wrong

• (1) That is the unit of the field itself. A line integral multiplies E by a length, adding a metre: N C⁻¹ m=J C⁻¹.
• (2) Also a unit of the field itself (volt per metre); integrating along a path in metres cancels the 'per metre', leaving volts.
• (4) That is the unit of ε₀, the permittivity of free space, which has nothing to do with integrating ⃗E along a path.

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