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What is the value of the loop integral [tex]\oint \mathbf{E} \cdot d\mathbf{l}[/tex]?

A. [tex]E \cdot l[/tex]
B. [tex]E \cdot dl[/tex]
C. [tex]E \times dl[/tex]
D. [tex]\oint E \times dl[/tex]

Answer :

Final answer:

The value of the loop integral ∮ E · dl vector is d) ∮ E · dl. The loop integral represents the line integral of the electric field E dotted with the infinitesimal displacement vector dl along a closed loop.

Explanation:

The value of the loop integral ∮ E · dl vector is d) ∮ E · dl.

The loop integral ∮ E · dl represents the line integral of the electric field E dotted with the infinitesimal displacement vector dl along a closed loop. Option d) ∮ E · dl is the correct option because it represents the dot product between the electric field and the infinitesimal displacement over the entire closed loop.

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