Question
Download Solution PDFThe time-independent electric field intensity is conservative in nature. Which of the following is true to satisfy this?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDF- The electric field intensity is conservative in nature and is depicted by ∇ × E = 0.
- The conservative nature of the electric field means that the line integral of the electric field along a closed path is zero.
\(\int_{a}^{b}\vec{E}.dl =0\)
Applying Stokes theorem:
\(\int_{a}^{b}\vec{E}.dl =\) \(\iint(\nabla\times E)ds\)
∇ × E = 0
The physical significance of the electrical field being conservative in nature:
- The work done to carry a test charge (q) from point A to another point B in the field due to Q does not depend upon the path followed.
- The electric field depends upon the initial and final positions A and B.
- Electric fields are independent of the path followed.
- So we say that the electric field is conservative in nature.
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