The work done to move a charge along an equipotential from A to B ______. a. cannot be defined as - int_A^B E.dl b. must be defined as - int_A^B E.dl c. is zero. d. can have a non-zero value.

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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` [Solution diagram: 326275_solution_1.png]

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