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Question
The work done to move a charge along an equipotential from A to B ______.
- cannot be defined as `- int_A^B E.dl`
- must be defined as `- int_A^B E.dl`
- is zero.
- can have a non-zero value.
Options
a and b
b and c
c and d
a and c
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Solution
b and c
Explanation:
The work done by the external agent in shifting the test charge along the dashed line from 1 to 2 is
|
The external agent does a work `W = - q int_1^2 vecE * vec(dl)` in transporting the test charge q slowly from the positions 1 to 2 in the static electric field. |
`W_("ext") = int_1^2 vecF_("ext") * vec(dl) int_1^2 (-qvecE) * vec(dl) = - q int_1^2 vecE * vec(dl)`
We know `V_A - V_B = - int_A^B vecE * vec(dl)` ......(i)
`W_("electrical") = -ΔU = - qΔV = q(V_A - V_B)` ......(ii)
Hence from (i) and (ii), `W_("electrical") = q(V_A - V_B) = - qint_A^B vecE * vec(dl)`
If we want to calculate the work done to move a charge along an equipotential from A to B
For equipotential surface VA = VB, hence W = 0
Also electric field is perpendicular to equipotential surface, hence `vecE * vec(dl) => W_("electrical") = 0`
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