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As per this diagram a point charge +q is placed at the origin O. Work done in taking another point charge - Q from the point A [co-ordinates (0, a)] to another point B [co-ordinates (a, 0)] along the straight path AB is :

  1. A
    zero
  2. B
    ((-qQ/4πε0)(1/a2)) √2a
  3. C
    ((qQ/4πε0)(1/a2)) . a/√2
  4. D
    ((qQ/4πε0)(1/a2)) √2a

Solution & Step-by-step Explanation

The work done in moving a charge in an electric field can be calculated using the formula W = ∫F·dl, where F is the force on the charge and dl is the displacement. For two point charges, the force between them is given by Coulomb's law, F = (kq1q2)/r^2, where k = 1/(4πε0), and r is the distance between the charges. The work done in moving a charge -Q from point A to point B in the presence of a charge +q at the origin can be found by integrating the force over the path AB. The distance between the charges varies as we move from A to B, but since the path is straight and in the first quadrant, we can use the distance formula to express r in terms of x (or y), where x ranges from 0 to a. However, without loss of generality and considering the symmetry of the problem, we can calculate the work done by considering the force at the midpoint of the path AB or by integrating over the path. The force on -Q due to +q is attractive and varies with the distance between the charges. The work done is given by the integral of the force over the distance, which can be simplified using the fact that the path is straight and the force can be resolved into components. The correct formula involves integrating the force over the path, considering the changing distance between the charges as we move from A to B. The work done is proportional to the product of the charges, inversely proportional to the square of the distance, and directly proportional to the displacement along the path. The exact calculation involves integrating the force over the path, which, due to the nature of the question, seems to be simplified or not fully detailed in the provided options.

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As per this diagram a point charge +q is placed at the origin O. Work done in taking another point charge - Q from the point A [co-ordinates (0, a)] to another point B [co-ordinates (a, 0)] along the straight path AB is :
A
zero
B
((-qQ/4πε0)(1/a2)) √2a
C
((qQ/4πε0)(1/a2)) . a/√2
D
((qQ/4πε0)(1/a2)) √2a

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